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On a new generalization of a Perov-type F-contraction with application to a semilinear operator system Fixed Point Theory Appl. Pub Date : 2024-03-18 Muhammad Sarwar, Syed Khayyam Shah, Kamaleldin Abodayeh, Arshad Khan, Ishak Altun
This manuscript aims to present new results about the generalized F-contraction of Hardy–Rogers-type mappings in a complete vector-valued metric space, and to demonstrate the fixed-point theorems for single and pairs of generalized F-contractions of Hardy–Rogers-type mappings. The established results represent a significant development of numerous previously published findings and results in the existing
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Fixed point theorem and iterated function system in φ-metric modular space Fixed Point Theory Appl. Pub Date : 2024-03-04 Bikramjit Acharjee, Guru Prem Prasad M
We introduce and study the concept of φ-metric modular space and, then define φ-α-Meir-Keeler contraction on it and explore its fixed point. Further, we define the Hausdorff distance between two non-empty compact subsets of the considered space. Some topological properties of φ-metric modular space are also explored. Additionally, we prove the existence of the attractor (fractal) of the IFS consisting
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Convergence results on the general inertial Mann–Halpern and general inertial Mann algorithms Fixed Point Theory Appl. Pub Date : 2023-12-08 Solomon Gebregiorgis, Poom Kumam
In this paper, we prove strong convergence theorem of the general inertial Mann–Halpern algorithm for nonexpansive mappings in the setting of Hilbert spaces. We also prove weak convergence theorem of the general inertial Mann algorithm for k-strict pseudo-contractive mappings in the setting of Hilbert spaces. These convergence results extend and generalize some existing results in the literature. Finally
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On a generalization of a relatively nonexpansive mapping and best proximity pair Fixed Point Theory Appl. Pub Date : 2023-11-27 Karim Chaira, Belkassem Seddoug
Let A and B be two nonempty subsets of a normed space X, and let $T: A \cup B \to A \cup B$ be a cyclic (resp., noncyclic) mapping. The objective of this paper is to establish weak conditions on T that ensure its relative nonexpansiveness. The idea is to recover the results mentioned in two papers by Matkowski (Banach J. Math. Anal. 2:237–244, 2007; J. Fixed Point Theory Appl. 24:70, 2022), by replacing
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Extending Snow’s algorithm for computations in the finite Weyl groups Fixed Point Theory Appl. Pub Date : 2023-11-20 Rafael Stekolshchik
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Random block-coordinate methods for inconsistent convex optimisation problems Fixed Point Theory Appl. Pub Date : 2023-11-06 Mathias Staudigl, Paulin Jacquot
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Fixed point theorems for enriched Kannan mappings in CAT(0) spaces Fixed Point Theory Appl. Pub Date : 2023-10-16 A. Y. Inuwa, P. Kumam, P. Chaipunya, S. Salisu
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Some fixed-point theorems of convex orbital \((\alpha, \beta )\)-contraction mappings in geodesic spaces Fixed Point Theory Appl. Pub Date : 2023-09-12 Rahul Shukla
The aim of this paper is to broaden the applicability of convex orbital $(\alpha, \beta )$ -contraction mappings to geodesic spaces. This class of mappings is a natural extension of iterated contraction mappings. The paper derives fixed-point theorems both with and without assuming continuity. Furthermore, the paper investigates monotone convex orbital $(\alpha, \beta )$ -contraction mappings and establishes
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Some applications of fixed point results for monotone multivalued and integral type contractive mappings Fixed Point Theory Appl. Pub Date : 2023-07-17 Nassar Aiman Majid, Alaa AL Jumaili, Zhen Chuan Ng, See Keong Lee
The motivation of the present paper is to introduce and establish some new fixed point results for monotone multivalued functions in partially ordered complete $D^{*}$ -metric spaces, where the partial ordered set $(X,\leq )$ is obtained via a pair of functions $( \Upsilon,\Omega )$ . Moreover, several existence and uniqueness coupled fixed point theorems of mappings satisfying contractive conditions
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Fixed point theorems and applications in p-vector spaces Fixed Point Theory Appl. Pub Date : 2023-07-03 George Xianzhi Yuan
The goal of this paper is to develop new fixed points for quasi upper semicontinuous set-valued mappings and compact continuous (single-valued) mappings, and related applications for useful tools in nonlinear analysis by applying the best approximation approach for classes of semiclosed 1-set contractive set-valued mappings in locally p-convex and p-vector spaces for $p \in (0, 1]$ . In particular
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Fixed-point results for fuzzy generalized β-F-contraction mappings in fuzzy metric spaces and their applications Fixed Point Theory Appl. Pub Date : 2023-06-12 Koon S. Wong, Zabidin Salleh, Che M. I. Che Taib
In this paper, we introduce fuzzy generalized β-F-contractions as a generalization of fuzzy F-contractions with admissible mappings. We deduce sufficient conditions for the existence and uniqueness of fixed points for fuzzy generalized β-F-contractions in complete strong fuzzy metric spaces. Our results generalize several fixed-point results from the literature. We present an application of our main
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A remark on Jleli–Samet’s best proximity point theorems for α-ψ-contraction mappings Fixed Point Theory Appl. Pub Date : 2023-06-05 Pinya Ardsalee
Inspired by the work of Jachymski, we slightly extend some fixed point theorems with a graph and show that some best proximity point theorems for α-ψ-contraction mappings of Jleli and Samet can be deduced by our results.
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Parametric quintic spline for time fractional Burger’s and coupled Burgers’ equations Fixed Point Theory Appl. Pub Date : 2023-06-01 D. A. Hammad, Mourad S. Semary, Ahmed G. Khattab
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Wellposedness and controllability results of stochastic integrodifferential equations with noninstantaneous impulses and Rosenblatt process Fixed Point Theory Appl. Pub Date : 2023-05-15 Ravikumar Kasinathan, Ramkumar Kasinathan, Varshini Sandrasekaran, Juan J. Nieto
The purpose of this work is to investigate a novel class of noninstantaneous impulsive stochastic integrodifferential equations (SIDEs) driven by Brownian motion and Rosenblatt process. We construct a new set of adequate assumptions for the existence and uniqueness of mild solutions using stochastic analysis, analytic semigroup theory, integral equation theory, and a fixed point methodology. Additionally
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Split monotone variational inclusion with errors for image-feature extraction with multiple-image blends problem Fixed Point Theory Appl. Pub Date : 2023-05-01 Pattanapong Tianchai
In this paper, we introduce a new iterative forward–backward splitting algorithm with errors for solving the split monotone variational inclusion problem of the sum of two monotone operators in real Hilbert spaces. We suggest and analyze this method under some mild appropriate conditions imposed on the parameters such that another strong convergence theorem for this problem is obtained. We also apply
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A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in Hadamard spaces Fixed Point Theory Appl. Pub Date : 2023-04-17 Kazeem Olalekan Aremu, Lateef Olakunle Jolaoso, Olawale Kazeem Oyewole
In this work, we study a self-adaptive extragradient algorithm for approximating a common solution of a pseudomonotone equilibrium problem and fixed-point problem for multivalued nonexpansive mapping in Hadamard spaces. Our proposed algorithm is designed in such a way that its step size does not require knowledge of the Lipschitz-like constants of the bifunction. Under some appropriate conditions,
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A Tseng-type algorithm for approximating zeros of monotone inclusion and J-fixed-point problems with applications Fixed Point Theory Appl. Pub Date : 2023-04-14 Abubakar Adamu, Poom Kumam, Duangkamon Kitkuan, Anantachai Padcharoen
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Convergence theorems for total asymptotically nonexpansive mappings in \(\operatorname{CAT} (\kappa )\) spaces Fixed Point Theory Appl. Pub Date : 2023-02-01 Shih-sen Chang, Liangcai Zhao, Min Liu, Jinfang Tang
The purpose of this paper is to study the convergence theorems in $\operatorname{CAT} (\kappa )$ spaces with $k > 0$ for total asymptotically nonexpansive mappings which are essentially wider than nonexpansive mappings, asymptotically nonexpansive mapping, and asymptotically nonexpansive mappings in the intermediate sense. Our results generalize, unify, and improve several comparable results in the
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Existence of solutions for Caputo fractional delay differential equations with nonlocal and integral boundary conditions Fixed Point Theory Appl. Pub Date : 2023-01-25 Ziyue Cui, Zongfu Zhou
In this paper, the existence and uniqueness of the solutions of Caputo fractional delay differential equations under nonlocal and integral boundary value conditions are studied. By using the Banach contraction principle and the Burton and Kirk fixed-point theorem, some new conclusions about the existence and uniqueness of solutions are obtained. An example is given to illustrate the main results.
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Fixed-point results for generalized contraction in K-sequentially complete ordered dislocated fuzzy quasimetric spaces Fixed Point Theory Appl. Pub Date : 2022-12-12 Shoaib, Abdullah, Khaliq, Kheeba
The ambition of this work is to introduce the notion of left (right) K-sequentially complete ordered dislocated fuzzy quasimetric spaces and to define a relevant Hausdorff metric on compact sets. A new approach, given in (Shoaib et al. in Filomat 34(2):323–338, 2020) has been used to obtain fixed-point results for multivalued mappings fulfilling generalized contraction in the latest framework. For
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Nonlinear analysis in p-vector spaces for single-valued 1-set contractive mappings Fixed Point Theory Appl. Pub Date : 2022-12-07 Yuan, George Xianzhi
The goal of this paper is to develop some fundamental and important nonlinear analysis for single-valued mappings under the framework of p-vector spaces, in particular, for locally p-convex spaces for $0 < p \leq 1$ . More precisely, based on the fixed point theorem of single-valued continuous condensing mappings in locally p-convex spaces as the starting point, we first establish best approximation
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Self-adaptive forward–backward splitting algorithm for the sum of two monotone operators in Banach spaces Fixed Point Theory Appl. Pub Date : 2022-12-06 Bello, Abdulmalik U., Chidume, Charles E., Alka, Maryam
In this work, we prove the weak convergence of a one-step self-adaptive algorithm to a solution of the sum of two monotone operators in 2-uniformly convex and uniformly smooth real Banach spaces. We give numerical examples in infinite-dimensional spaces to compare our result with some existing algorithms. Finally, our results extend and complement several existing results in the literature.
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Solving nonlinear and dynamic programming equations on extended b-metric spaces with the fixed-point technique Fixed Point Theory Appl. Pub Date : 2022-12-01 Belhenniche, Abdelkader, Guran, Liliana, Benahmed, Sfya, Lobo Pereira, Fernando
In this article, we present an approach to solve a wide range of nonlinear equations formulated in extended b-metric spaces based on a new fixed-point theorem on these spaces. This research effort was motivated by challenges arising in solving pattern problems efficiently that can not be addressed by using standard metric spaces. Our approach relies on a novel common fixed-point theorem for Ćirić-type
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Existence of common fixed point in Kannan F-contractive mappings in quasi-partial b-metric space with an application Fixed Point Theory Appl. Pub Date : 2022-11-21 Gautam, Pragati, Kumar, Santosh, Verma, Swapnil, Gupta, Gauri
The purpose of this study is to demonstrate results on fixed point theory in quasi-partial b-metric space recognizing a new type of mapping, which is a blend of F-contraction and Kannan contraction, and to establish the fixed point results in F-expanding type mappings. Additionally, the obtained results are the application of the contractive mappings to functional equations. Furthermore, Mathematica
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A new continuous hybrid block method with one optimal intrastep point through interpolation and collocation Fixed Point Theory Appl. Pub Date : 2022-11-14 Tassaddiq, Asifa, Qureshi, Sania, Soomro, Amanullah, Hincal, Evren, Shaikh, Asif Ali
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Solving an integral equation via generalized controlled fuzzy metrics Fixed Point Theory Appl. Pub Date : 2022-11-01 Mani, Gunaseelan, Gnanaprakasam, Arul Joseph, Dinmohammadi, Abdollah, Parvaneh, Vahid, Mohammadi, Babak
The purpose of this manuscript is to obtain some fixed point results in generalized controlled fuzzy metric spaces. Our results generalize and extend many of the previous findings in the same approach. Moreover, two examples to support our theorems are obtained. Finally, to examine and strengthen the theoretical results, the existence and uniqueness of the solution to a nonlinear integral equation
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Nonlinear analysis by applying best approximation method in p-vector spaces Fixed Point Theory Appl. Pub Date : 2022-10-12 Yuan, George Xianzhi
It is known that the class of p-vector spaces $(0 < p \leq 1)$ is an important generalization of the usual norm spaces with rich topological and geometrical structure, but most tools and general principles with nature in nonlinearity have not been developed yet. The goal of this paper is to develop some useful tools in nonlinear analysis by applying the best approximation approach for the classes of
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Unified primal-dual active set method for dynamic frictional contact problems Fixed Point Theory Appl. Pub Date : 2022-08-30 Abide, Stéphane, Barboteu, Mikaël, Cherkaoui, Soufiane, Dumont, Serge
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Solving an integral equation via \(\mathscr{C}^{\star}\)-algebra-valued partial b-metrics Fixed Point Theory Appl. Pub Date : 2022-07-11 Maheswari, J. Uma, Anbarasan, A., Gunaseelan, M., Parvaneh, V., Bonab, S. Hadi
In this paper, we prove some common coupled fixed-point theorems on complete $\mathscr{C}^{\star}$ -algebra-valued partial b-metric spaces. Some of the well-known facts in the literature are generalized and expanded by the results shown. An example to illustrate our findings is presented. We also explore some of the applications of our key results.
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Penalty method for a class of differential nonlinear system arising in contact mechanics Fixed Point Theory Appl. Pub Date : 2022-07-04 Chu, Xu, Chen, Tao, Huang, Nan-jing, Xiao, Yi-bin
The main goal of this paper is to study a class of differential nonlinear system involving parabolic variational and history-dependent hemivariational inequalities in Banach spaces by using the penalty method. We first construct a penalized problem for such a nonlinear system and then derive the existence and uniqueness of its solution to obtain an approximating sequence for the nonlinear system. Moreover
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On a class of generalized saddle-point problems arising from contact mechanics Fixed Point Theory Appl. Pub Date : 2022-06-27 Matei, Andaluzia
In the present paper we consider a class of generalized saddle-point problems described by means of the following variational system: $$\begin{aligned} &a(u,v-u)+b(v-u,\lambda )+j(v)-j(u)+J(u,v)-J(u,u)\geq (f,v-u)_{X}, \\ &b(u,\mu -\lambda )-\psi (\mu )+\psi (\lambda )\leq 0, \end{aligned}$$ ( $v\in K\subseteq X$ , $\mu \in \Lambda \subset Y$ ), where $(X,(\cdot,\cdot )_{X})$ and $(Y,(\cdot,\cdot )_{Y})$
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Analysis of a debonding model of two elastic 2D-bars Fixed Point Theory Appl. Pub Date : 2022-06-06 Shillor, Meir, Kuttler, Kenneth L.
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On a nonlinear elasticity problem with friction and Sobolev spaces with variable exponents Fixed Point Theory Appl. Pub Date : 2022-06-01 Boukrouche, Mahdi, Merouani, Boubakeur, Zoubai, Fayrouz
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Fixed point theorems for generalized \((\alpha ,\psi )\)-contraction mappings in rectangular quasi b-metric spaces Fixed Point Theory Appl. Pub Date : 2022-05-02 Abagaro, Bontu Nasir, Tola, Kidane Koyas, Mamud, Mustefa Abduletif
In this paper, we introduce the class of rectangular quasi b-metric spaces as a generalization of rectangular metric spaces, rectangular quasi-metric spaces, rectangular b-metric spaces, define generalized $(\alpha ,\psi ) $ -contraction mappings and study fixed point results for the maps introduced in the setting of rectangular quasi b-metric spaces. Our results extend and generalize related fixed
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A contact problem for a piezoelectric actuator on an elasto-plastic obstacle Fixed Point Theory Appl. Pub Date : 2022-04-11 Krejčí, Pavel, Petrov, Adrien
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Tykhonov well-posedness of fixed point problems in contact mechanics Fixed Point Theory Appl. Pub Date : 2022-04-04 Sofonea, Mircea
We consider a fixed point problem $\mathcal {S}u=u$ where ${\mathcal {S}:C(\mathbb{R}_{+};X)\to C(\mathbb{R}_{+};X)}$ is an almost history-dependent operator. First, we recall the unique solvability of the problem. Then, we introduce the concept of Tykhonov triple, provide several relevant examples, and prove the corresponding well-posedness results for the considered fixed point problem. This allows
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A priori error analysis of virtual element method for contact problem Fixed Point Theory Appl. Pub Date : 2022-04-01 Wang, Fei, Reddy, B. Daya
As an extension of the finite element method, the virtual element method (VEM) can handle very general polygonal meshes, making it very suitable for non-matching meshes. In (Wriggers et al. in Comput. Mech. 58:1039–1050, 2016), the lowest-order virtual element method was applied to solve the contact problem of two elastic bodies on non-matching meshes. The numerical experiments showed the robustness
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An inertial s-iteration process for a common fixed point of a family of quasi-Bregman nonexpansive mappings Fixed Point Theory Appl. Pub Date : 2022-03-14 Ali, Bashir, Adam, Aisha A.
In this paper, an inertial S-iteration iterative process for approximating a common fixed point of a finite family of quasi-Bregman nonexpansive mappings is introduced and studied in a reflexive Banach space. A strong convergence theorem is proved. Some applications of the theorem are presented. The results presented here improve, extend, and generalize some recent results in the literature.
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Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces Fixed Point Theory Appl. Pub Date : 2022-03-07 Minjibir, Ma’aruf Shehu, Izuazu, Chimezie
Let E be a strictly convex real Banach space and let $D\subseteq E$ be a nonempty closed convex subset of E. Let $T_{i}: {D}\longrightarrow \mathcal{P}({D})$ , $i=1,2,3,\ldots $ be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric, $\mathcal{P}(D)$ is the family of proximinal and bounded subsets of D. Supposing that the family has at least
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Neutral functional sequential differential equations with Caputo fractional derivative on time scales Fixed Point Theory Appl. Pub Date : 2022-03-01 Lazreg, Jamal Eddine, Benkhettou, Nadia, Benchohra, Mouffak, Karapinar, Erdal
In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray–Schauder type and Krasnoselskii fixed point theorem. As applications, two examples are included to show the applicability
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A remark on Secelean–Wardowski’s fixed point theorems Fixed Point Theory Appl. Pub Date : 2022-02-21 Saejung, Satit, Ardsalee, Pinya
In this paper we give a simple proof of three fixed point theorems of Secelean and Wardowski by using the fixed point result of Jachymski et al. Our result is established with weaker assumptions than the three theorems. Furthermore, the recent result of Secelean et al. in the setting of a complete metric space can be also deduced by our theorem.
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History-dependent operators and prox-regular sweeping processes Fixed Point Theory Appl. Pub Date : 2022-02-14 Nacry, Florent, Sofonea, Mircea
We consider an abstract inclusion in a real Hilbert space, governed by an almost history-dependent operator and a time-dependent multimapping with prox-regular values. We establish the unique solvability of the inclusion under appropriate assumptions on the data. The proof is based on the arguments of monotonicity, fixed point, and prox-regularity. We then use our result in order to deduce some direct
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Existence of solutions for a Lipschitzian vibroimpact problem with time-dependent constraints Fixed Point Theory Appl. Pub Date : 2022-02-01 Adly, Samir, Thieu, Nguyen Nang
We study a mechanical system with a finite number of degrees of freedom, subjected to perfect time-dependent frictionless unilateral (possibly nonconvex) constraints with inelastic collisions on active constraints. The dynamic is described in the form of a second-order measure differential inclusion. Under some regularity assumptions on the data, we establish several properties of the set of admissible
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From the Fan-KKM principle to extended real-valued equilibria and to variational-hemivariational inequalities with application to nonmonotone contact problems Fixed Point Theory Appl. Pub Date : 2022-01-31 Gwinner, Joachim
This paper starts off by the celebrated Knaster–Kuratowski–Mazurkiewicz principle in the formulation by Ky Fan. We provide a novel variant of this principle and build an existence theory for extended real-valued equilibrium problems with general, then monotone and pseudomonotone bifunctions. We develop our existence theory first in general topological vector spaces, then in reflexive Banach spaces
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Unsteady non-Newtonian fluid flow with heat transfer and Tresca’s friction boundary conditions Fixed Point Theory Appl. Pub Date : 2022-01-24 Paoli, Laetitia
We consider an unsteady non-isothermal flow problem for a general class of non-Newtonian fluids. More precisely the stress tensor follows a power law of parameter p, namely $\sigma = 2 \mu ( \theta , \upsilon , \| D(\upsilon ) \|) \|D( \upsilon ) \|^{p-2} D(\upsilon ) - \pi \mathrm{Id}$ where θ is the temperature, π is the pressure, υ is the velocity, and $D(\upsilon )$ is the strain rate tensor of
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Circumcentering approximate reflections for solving the convex feasibility problem Fixed Point Theory Appl. Pub Date : 2022-01-04 Araújo, G. H. M., Arefidamghani, R., Behling, R., Bello-Cruz, Y., Iusem, A., Santos, L.-R.
The circumcentered-reflection method (CRM) has been applied for solving convex feasibility problems. CRM iterates by computing a circumcenter upon a composition of reflections with respect to convex sets. Since reflections are based on exact projections, their computation might be costly. In this regard, we introduce the circumcentered approximate-reflection method (CARM), whose reflections rely on
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On compositions of special cases of Lipschitz continuous operators Fixed Point Theory Appl. Pub Date : 2021-12-20 Giselsson, Pontus, Moursi, Walaa M.
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous
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Numerical analysis of doubly-history dependent variational inequalities in contact mechanics Fixed Point Theory Appl. Pub Date : 2021-12-13 Xu, Wei, Wang, Cheng, He, Mingyan, Chen, Wenbin, Han, Weimin, Huang, Ziping
This paper is devoted to numerical analysis of doubly-history dependent variational inequalities in contact mechanics. A fully discrete method is introduced for the variational inequalities, in which the doubly-history dependent operator is approximated by repeated left endpoint rule and the spatial variable is approximated by the linear element method. An optimal order error estimate is derived under
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Projecting onto rectangular matrices with prescribed row and column sums Fixed Point Theory Appl. Pub Date : 2021-12-06 Bauschke, Heinz H., Singh, Shambhavi, Wang, Xianfu
In 1990, Romero presented a beautiful formula for the projection onto the set of rectangular matrices with prescribed row and column sums. Variants of Romero’s formula were rediscovered by Khoury and by Glunt, Hayden, and Reams for bistochastic (square) matrices in 1998. These results have found various generalizations and applications. In this paper, we provide a formula for the more general problem
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Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality Fixed Point Theory Appl. Pub Date : 2021-12-01 Ling, Min, Han, Weimin
This paper provides a well-posedness analysis for a hemivariational inequality of the stationary Navier-Stokes equations by arguments of convex minimization and the Banach fixed point. The hemivariational inequality describes a stationary incompressible fluid flow subject to a nonslip boundary condition and a Clarke subdifferential relation between the total pressure and the normal component of the
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Feasibility-based fixed point networks Fixed Point Theory Appl. Pub Date : 2021-11-22 Heaton, Howard, Wu Fung, Samy, Gibali, Aviv, Yin, Wotao
Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable recovery with respect to data perturbations. Hand-chosen analytic regularization can yield desirable theoretical guarantees, but such approaches have limited effectiveness
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Market equilibria and money Fixed Point Theory Appl. Pub Date : 2021-11-15 Flåm, Sjur Didrik
By the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generalizing the second welfare theorem we show that the said solutions may coincide as a common fixed point for one and the same system. Mathematical arguments invoke conjugation, convolution, and
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Analysis of Stokes system with solution-dependent subdifferential boundary conditions Fixed Point Theory Appl. Pub Date : 2021-11-08 Zhao, Jing, Migórski, Stanisław, Dudek, Sylwia
We study the Stokes problem for the incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier–Fujita slip condition, and the threshold slip and leak condition of frictional type. The weak form of the problem leads to a new class of variational–hemivariational
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An improved fast iterative shrinkage thresholding algorithm with an error for image deblurring problem Fixed Point Theory Appl. Pub Date : 2021-11-01 Tianchai, Pattanapong
In this paper, we introduce a new iterative forward-backward splitting method with an error for solving the variational inclusion problem of the sum of two monotone operators in real Hilbert spaces. We suggest and analyze this method under some mild appropriate conditions imposed on the parameters such that another strong convergence theorem for these problem is obtained. We also apply our main result
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Asymptotic behavior of Newton-like inertial dynamics involving the sum of potential and nonpotential terms Fixed Point Theory Appl. Pub Date : 2021-10-18 Adly, Samir, Attouch, Hedy, Vo, Van Nam
In a Hilbert space $\mathcal{H}$ , we study a dynamic inertial Newton method which aims to solve additively structured monotone equations involving the sum of potential and nonpotential terms. Precisely, we are looking for the zeros of an operator $A= \nabla f +B $ , where ∇f is the gradient of a continuously differentiable convex function f and B is a nonpotential monotone and cocoercive operator
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An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator Fixed Point Theory Appl. Pub Date : 2021-10-04 Dao, Minh N., Phan, Hung M.
Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm for finding a zero of the sum of three operators. We assume that two of the operators
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A generalized multivariable Newton method Fixed Point Theory Appl. Pub Date : 2021-09-20 Burachik, Regina S., Caldwell, Bethany I., Kaya, C. Yalçın
It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a larger convergence region as well as more desirable properties near a solution. We prove quadratic convergence of the new family, and provide specific bounds for the
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Strongly regular points of mappings Fixed Point Theory Appl. Pub Date : 2021-09-06 Abbasi, Malek, Théra, Michel
In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of a given mapping at a certain point. Then, we discuss the Hoffman estimation and achieve some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows one to calculate the coefficient
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Convergence of proximal splitting algorithms in \(\operatorname{CAT}(\kappa)\) spaces and beyond Fixed Point Theory Appl. Pub Date : 2021-08-24 Lauster, Florian, Luke, D. Russell
In the setting of $\operatorname{CAT}(\kappa)$ spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky–Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric subregularity. Linear metric subregularity is in any case necessary for linearly convergent fixed point sequences, so the result is tight. To show this
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Learning without loss Fixed Point Theory Appl. Pub Date : 2021-07-26 Veit Elser
We explore a new approach for training neural networks where all loss functions are replaced by hard constraints. The same approach is very successful in phase retrieval, where signals are reconstructed from magnitude constraints and general characteristics (sparsity, support, etc.). Instead of taking gradient steps, the optimizer in the constraint based approach, called relaxed–reflect–reflect (RRR)