We study a source identification problem for a parabolic equation with multipoint nonlocal boundary condition. Stability estimates for the solution of abstract source identification problem are established. In application, stability estimates for the solution of the overdetermined mixed boundary value problem for multidimensional parabolic equation are obtained. The first and second order of accuracy

We consider an optimal control problem Q governed by an elliptic quasivariational inequality with unilateral constraints. We associate to Q a new optimal control problem Q˜, obtained by perturbing the state inequality (including the set of constraints and the nonlinear operator) and the cost functional, as well. Then, we provide sufficient conditions which guarantee the convergence of solutions of

Abstract In this paper, we consider convex Tikhonov regularization for the solution of linear operator equations on Hilbert spaces. We show that standard fractional source conditions can be employed in order to derive convergence rates in terms of the Bregman distance, assuming some stronger convexity properties of either the regularization term or its convex conjugate. In the special case of quadratic

The goal of this paper is to develop a framework that would allow one to solve the problems of optimal recovery of the monotone operators that act on a possibly most extensive class of monotone functions. The results of this work allow us to include the operators that act on the spaces of multi- and fuzzy- valued functions, as well as on the spaces of functions with values in partially ordered normed

In this paper, we study a Thakur three-step iterative process in the new context of generalized nonexpansive mappings enriched with property (E). A uniformly convex Banach space is used as underlying setting for our approach. In order to emphasize our results we offer an example of a mapping on R2 endowed with property (E) that exceeds the well known class of Suzuki mappings. By connecting the Thakur

Newton’s method is usually preferred when solving optimization problems due to its superior convergence properties compared to gradient-based or derivative-free optimization algorithms. However, deriving and computing second-order derivatives needed by Newton’s method often is not trivial and, in some cases, not possible. In such cases quasi-Newton algorithms are a great alternative. In this paper

The Peterlin viscoelastic model describes the motion of certain incompressible polymeric fluids. It employs a nonlinear dumbbell model with a nonlinear spring force law making it more nonlinear than other viscoelastic models. In this paper, we propose and study a fully implicit stabilized Crank-Nicolson time stepping scheme for finite element spatial discretization of the non-stationary Peterlin viscoelastic

We consider a quadratic optimal control problem for the 3D Navier-Stokes-Voigt equations with periodic inputs. We prove the existence of optimal solutions, then establish necessary and sufficient optimality conditions. We also define semidiscrete-in-time approximations for the optimal control problem and then prove the existence of a subsequence that converges to an optimal solution.

We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain higher regularity for the optimal state under appropriate assumptions on the data. We also solve the optimal control problem as a fourth order variational inequality

We study the proximal point method for solving quasi-equilibrium problems in Banach spaces, which generalizes the proximal point method for equilibrium problems and quasi-variational inequalities. We propose a regularization procedure which ensures strong convergence of the generated sequence to a solution of the quasi-equilibrium problem, under standard assumptions on the problem without assuming

The current article intends to study some elementary constrained approximation aspects of the bivariate fractal functions. To this end, firstly the construction of bivariate fractal interpolation functions available in the literature is revisited with a focus to obtain a parameterized family of fractal functions corresponding to a prescribed bivariate continuous function on a rectangular region in

The influence of errors on the convergence of infinite products of weak quasi-contraction mappings in b-metric spaces is explored. An example demonstrating the necessity of convergence of the sequence of computational errors to zero is also provided. Moreover, we discuss weak ergodic theorems in the setting of b-metric spaces.

In this article, we consider optimal control problems for the one-dimensional Frémond model for shape memory alloys. This model is constructed in terms of basic functionals like free energy and pseudo-potential of dissipation. The state problem is expressed by a system of partial differential equations involving the balance equations for energy and momentum. We prove the existence of an optimal control

In this work, the boundedness and essential norm of weighted composition operators from the Zygmund space to nth weighted-type spaces are characterized. As a corollary, some characterizations for the compactness of weighted composition operators from the Zygmund space to nth weighted-type spaces are also presented.

In this paper, we present a numerical verification method of solutions for nonlinear parabolic initial boundary value problems. Decomposing the problem into a nonlinear part and an initial value part, we apply Nakao’s projection method, which is based on the full-discrete finite element method with constructive error estimates, to the nonlinear part and use the theoretical analysis for the heat equation

The goal of this paper is to develop a framework that would allow one to solve the problems of optimal recovery of the monotone operators that act on a possibly most extensive class of monotone functions. The results of this work allow us to include the operators that act on the spaces of multi- and fuzzy- valued functions, as well as on the spaces of functions with values in partially ordered normed

The approximation of functions using linear positive operators is affected by saturation. The quality of approximation offered by iterated Boolean sums increases with the regularity of the function. We present some qualitative and quantitative results concerning the approximation by such Boolean sums. The general results are illustrated by examples.

The article presents an explicit form for the second moment of cubic Schoenberg operators with arbitrary knots and in the particular case of equidistant knots. Applications are given for quantitative direct results in approximation and in construction of special classes of Schoenberg operators.

In this paper, we use the upward power preorder relation on the power sets of ordered sets to construct a mathematical social benefit maximization model in a fiscal year with respect to the initially planned fiscal budgetary policies and the practically implementation of the fiscal budgetary policies. We only consider the uncertainty case for the social benefit functions. By applying the Fan-KKM Theorem

In this paper, we study the sampling and average sampling problem in a quasi shift-invariant space VX(φ), where X is a discrete subset of R and φ is a continuously differentiable positive definite function satisfying certain decay conditions. We show that any f belonging to VX(φ) can be uniquely and stably reconstructed from its samples {f(yk):k∈Z} as well as from its average samples provided sampling

In this article, it is concerned existence of solutions to a class of nonlinear system of fractional differential equations. It is proved the existence of at least three different weak solutions through the critical point theory and the variational method. In this way, it is applied well-known theorem proved by Bonanno and Marano on the construction of the critical set of functionals with a weak compactness

This note presents ad-nonprojection method for approximation to infinite-dimensional Moore-Penrose inverse, which includes generalized projection method as a special case. The main result (Theorem 4) gives characteristics of perfect convergence, weak perfect convergence, and uniform perfect convergence of ad-nonprojection method. This result is a generalization of several fundamental theorems known

We derive and analyze a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a black box, which is used to define the iteration process. We prove convergence and stability for the scheme in infinite dimensional Hilbert spaces. These theoretical

In this paper, using the hybrid method defined by Nakajo and Takahashi, we first obtain a strong convergence theorem for two noncommutative generic skew generalized nonspreading mappings in a Banach space. Next, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove another strong convergence theorem for the mappings in a Banach space. Using these results, we get

In this article, we will present some results relating sharp ordering (a≤♯b) and investigate the properties of one-sided cyclic ideals in rings. Necessary and sufficient conditions for the invertibility and the group invertibility of the linear combination c1a+c2b are given, where a is below b under the sharp order, a and b are elements of an algebra, and c1, c2 are elements of an arbitrary field.

The Zhang neural network (ZNN), a recurrent neural network, proposed in 2001, is particularly effective in solving time-varying problems. It has shown high efficiency and excellent performance in various applications. The weighted pseudoinverse is a useful tool in solving and analyzing the constrained least-squares problems. In this paper, we propose a ZNN model for computing the weighted pseudoinverse

Here, we study the numerical solution of singularly perturbed system of two-point boundary-value problems of reaction-diffusion type. The solutions of these problems exhibit twin overlapping exponential boundary layers. To obtain the numerical solutions of these problems, we apply the nonsymmetric discontinuous Galerkin FEM with interior penalties (NIPG method) on layer-adapted piecewise-uniform Shishkin

We study variational inequalities which are governed by a strongly monotone and Lipschitz continuous operator F over a closed and convex set S. We assume that S=C∩A−1(Q) is the nonempty solution set of a (multiple-set) split convex feasibility problem, where C and Q are both closed and convex subsets of two real Hilbert spaces H1 and H2, respectively, and the operator A acting between them is linear

In a recent paper of Cuenya and Ferreyra, a condition, namely, the Cp-condition in Lp-spaces was introduced that is weaker than the notion of Lp-derivative given by Calderón-Zygmund. In the present article, we define the Legendre derivative for functions in L2 generalizing both notions, the Cp-condition and Lp-derivative in the case p = 2. As a consequence, we give a necessary and sufficient condition

In this paper, we introduce a novel algorithm for finding a common point of the solution set of a class of equilibrium problems involving pseudo-monotone bifunctions and satisfying the Lipschitz-type condition and the set of fixed points of a quasi-nonexpansive in a real Hilbert space. This algorithm can be considered as a combination of the subgradient extragradient method for equilibrium problems

This article mainly studies the nonuniform and semi-average sampling of time-varying shift-invariant signals living in a mixed Lebesgue space Lp,q(Rd+1), under the condition that the generator φ of the shift-invariant subspace belongs to a hybrid-norm space of mixed form depending on the orders p and q. First, the sampling stability for two kinds of semi-average sampling functionals is established

In this paper, we consider the nonconvex quadratic optimization problem with a single quadratic constraint. First we give a theoretical characterization of the local non-global minimizers. Then we extend the recent characterization of the global minimizer via a generalized eigenvalue problem to the local non-global minimizers. Finally, we use these results to derive an efficient algorithm that finds

In the current paper, we discuss sufficient and necessary conditions for the existence of best proximity points for cyclic f- contractive mappings in the setting of strictly convex Banach spaces. Extensions of Edelstein’s theorem are considered as well as an extension of a main result in Park [Park, S. (1978). Fixed points of f-contractive maps. Rocky Mountain J. Math. 8:743–750]. Another existence

Given a positive weight function and an isometry map on a Hilbert spaces H, we study a class of linear maps which is a g-frame, g-Riesz basis, and a g-orthonormal basis for H with respect to C in terms of the weight function. We apply our results to study the frame for shift-invariant subspaces on the Heisenberg group.

In this paper, we apply, to the case of approximate minimizers for vector optimization problems with set-valued maps, some techniques developed previously in literature for the situation of standard vector efficiency. The approach we propose here allows us, on one hand, to extend some known results, and, on the other hand, to emphasize some numerical aspects that could be of certain importance for

In this paper, we extend the study of an iteration process introduced by Thakur-Thakur-Postolache [J. Inequal. Appl., (2014), 147–155] from the class of nonexpansive operators to the more general class of Suzuki operators. We prove weak and strong convergence theorems regarding the iteration method for mappings satisfying the condition (C) of Suzuki in uniformly convex Banach spaces. We study the stability

Several logarithmic-barrier interiors-point methods are now available for solving two-stage stochastic optimization problems with recourse in the finite-dimensional setting. However, despite the genuine need for studying such methods in general spaces, there are no infinite-dimensional analogs of these methods. Inspired by this evident gap in the literature, in this paper, we propose logarithmic-barrier

In the context of convex variational regularization, it is a known result that, under suitable differentiability assumptions, source conditions in the form of variational inequalities imply range conditions, while the converse implication only holds under an additional restriction on the operator. In this article, we prove the analogous result for polyconvex regularization. More precisely, we show

In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection

For the solution of operator equations, Stevenson introduced a definition of frames, where a Hilbert space and its dual are not identified. This means that the Riesz isomorphism is not used as an identification, which, for example, does not make sense for the Sobolev spaces H 0 1 ( Ω ) and H - 1 ( Ω ) . In this article, we are going to revisit the concept of Stevenson frames and introduce it for Banach