-
Degeneration phenomenon in linear ordinary differential equations Georgian Math. J. (IF 0.7) Pub Date : 2024-02-20 Vakhtang Lomadze
Given a linear constant coefficient ODE depending on a parameter, when this parameter approaches zero, the solution set converges to the solution set of the limit differential equation if the leading coefficient does not vanish. The situation is very subtle in the singular case, i.e., in the case when this coefficient becomes zero. The solution set then may even collapse completely. In this note, a
-
Fractional p-Laplacian elliptic Dirichlet problems Georgian Math. J. (IF 0.7) Pub Date : 2024-02-20 David Barilla, Martin Bohner, Giuseppe Caristi, Fariba Gharehgazlouei, Shapour Heidarkhani
In this paper, we consider a fractional p-Laplacian elliptic Dirichlet problem that possesses one control parameter and has a Lipschitz nonlinearity order of p - 1 {p-1} . The multiplicity of the weak solutions is proved by means of the variational method and critical point theory. We investigate the existence of at least three solutions to the problem.
-
On perturbation of continuous frames in Hilbert C *-modules Georgian Math. J. (IF 0.7) Pub Date : 2024-02-20 Hadi Ghasemi, Tayebe Lal Shateri
In the present paper, we examine the perturbation of continuous frames and Riesz-type frames in Hilbert C * {C^{*}} -modules. We extend the Casazza–Christensen general perturbation theorem for Hilbert space frames to continuous frames in Hilbert C * {C^{*}} -modules. We obtain a necessary condition under which the perturbation of a Riesz-type frame of Hilbert C * {C^{*}} -modules remains to be a Riesz-type
-
A generalization of Hardy’s inequality to infinite tensors Georgian Math. J. (IF 0.7) Pub Date : 2024-02-20 Morteza Saheli, Davoud Foroutannia, Sara Yusefian
In this paper, we extend Hardy’s inequality to infinite tensors. To do so, we introduce Cesàro tensors ℭ {\mathfrak{C}} , and consider them as tensor maps from sequence spaces into tensor spaces. In fact, we prove inequalities of the form ∥ ℭ x k ∥ t , 1 ≤ U ∥ x ∥ l p k \|\mathfrak{C}x^{k}\|_{t,1}\leq U\|x\|_{l_{p}}^{k} ( k = 1 , 2 k=1,2 ), where x is a sequence, ℭ x k {\mathfrak{C}x^{k}} is
-
Busemann--Petty-type problem for μ-intersection bodies Georgian Math. J. (IF 0.7) Pub Date : 2024-02-20 Chao Li, Gangyi Chen
The Busemann–Petty problem of arbitrary measure for symmetric star bodies is proposed and studied by Zvavitch, which is a generalization of the classical Busemann–Petty problem. In this paper, we study the Busemann–Petty-type problem for homogeneous measure for general star bodies.
-
Analytic solution to functional differential equations via Bell’s polynomials Georgian Math. J. (IF 0.7) Pub Date : 2024-02-20 Diego Caratelli, Pierpaolo Natalini, Paolo Emilio Ricci
It is shown how to approximate the solution of functional differential equations in terms of Bell’s polynomials. Some numerical checks are shown, by using the computer algebra system Mathematica © {{}^{\copyright}} .
-
On the correspondence between periodic solutions of differential and dynamic equations on periodic time scales Georgian Math. J. (IF 0.7) Pub Date : 2024-02-08 Viktoriia Tsan, Oleksandr Stanzhytskyi, Olha Martynyuk
This paper studies the relationship between the existence of periodic solutions of systems of dynamic equations on time scales and their corresponding systems of differential equations. We have established that, for a sufficiently small graininess function, if a dynamic equation on a time scale has an asymptotically stable periodic solution, then the corresponding differential equation will also have
-
V_a -deformed free convolution and variance function Georgian Math. J. (IF 0.7) Pub Date : 2024-01-31 Raouf Fakhfakh
In this paper, we deal with the notion of V a {V_{a}} -deformed free convolution, introduced in [A. D. Krystek and L. J. Wojakowski, Associative convolutions arising from conditionally free convolution, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8 2005, 3, 515–545], from a point of view related to the theory of Cauchy–Stieltjes kernel (CSK) families and their corresponding variance functions
-
Finite groups in which some particular invariant subgroups are TI-subgroups or subnormal subgroups Georgian Math. J. (IF 0.7) Pub Date : 2024-01-30 Yifan Liu, Jiangtao Shi
Let A and G be finite groups such that A acts coprimely on G by automorphisms. We prove that if every self-centralizing non-nilpotent A-invariant subgroup of G is a TI-subgroup or a subnormal subgroup, then every non-nilpotent A-invariant subgroup of G is subnormal and G is p-nilpotent or p-closed for any prime divisor p of | G | {|G|} . If every self-centralizing non-metacyclic A-invariant subgroup
-
Generalized essential spectra involving the class of g-g-Riesz operators Georgian Math. J. (IF 0.7) Pub Date : 2024-01-30 Imen Ferjani, Omaima Kchaou, Bilel Krichen
In this paper, we explore the spectral properties of unbounded generalized Fredholm operators acting on a non-reflexive Banach space X. The results are formulated in terms of some topological conditions made on X or on its dual X * {X^{*}} . In addition, we introduce the concept of the so-called g-g-Riesz linear operators as an extension of Riesz operators. The obtained results are used to discuss
-
On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition Georgian Math. J. (IF 0.7) Pub Date : 2024-01-10 Abdeljalil Nachaoui, Tea Shavadze, Tamaz Tadumadze
The analytic relation between solutions of the original Cauchy problem and a corresponding perturbed problem is established. In the representation formula of solution, the effects of the discontinuous initial condition and perturbation of the initial data are revealed.
-
A note on b-generalized (α,β)-derivations in prime rings Georgian Math. J. (IF 0.7) Pub Date : 2024-01-04 Nripendu Bera, Basudeb Dhara
Let R be a prime ring, let 0 ≠ b ∈ R {0\neq b\in R} , and let α and β be two automorphisms of R. Suppose that F : R → R {F:R\rightarrow R} , F 1 : R → R {F_{1}:R\rightarrow R} are two b-generalized ( α , β ) {(\alpha,\beta)} -derivations of R associated with the same ( α , β ) {(\alpha,\beta)} -derivation d : R → R d:R\rightarrow R , and let G : R → R G:R\rightarrow R be a b-generalized ( α , β ) (\alpha
-
Numerical approaches for solution of hyperbolic difference equations on circle Georgian Math. J. (IF 0.7) Pub Date : 2024-01-03 Allaberen Ashyralyev, Fatih Hezenci, Yasar Sozen
The present paper considers nonlocal boundary value problems for hyperbolic equations on the circle T 1 \mathbb{T}^{1} . The first-order modified difference scheme for the numerical solution of nonlocal boundary value problems for hyperbolic equations on a circle is presented. The stability and coercivity estimates in various Hölder norms for solutions of the difference schemes are established. Moreover
-
Essential norm of Riemann–Stieltjes operator on weighted Bergman spaces with doubling weights Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Lian Hu, Songxiao Li, Rong Yang
Let ω be a doubling weight and 0 < p ≤ q < ∞ {0
-
Representations of a number in an arbitrary base with unbounded digits Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Artūras Dubickas
In this paper, we prove that, for β ∈ ℂ {\beta\in{\mathbb{C}}} , every α ∈ ℂ {\alpha\in{\mathbb{C}}} has at most finitely many (possibly none at all) representations of the form α = d n β n + d n - 1 β n - 1 + … + d 0 {\alpha=d_{n}\beta^{n}+d_{n-1}\beta^{n-1}+\dots+d_{0}} with nonnegative integers n , d n , d n - 1 , … , d 0 {n,d_{n},d_{n-1},\dots,d_{0}} if and only if β is a transcendental number
-
On φ-u-S-flat modules and nonnil-u-S-injective modules Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Hwankoo Kim, Najib Mahdou, El Houssaine Oubouhou
This paper introduces and studies the ϕ-u-S-flat (resp., nonnil-u-S-injective) modules, which are a generalization of both ϕ-flat modules and u-S-flat modules (resp., both nonnil-injective modules and u-S-injective modules). We give the Cartan–Eilenberg–Bass theorem for nonnil-u-S-Noetherian rings. Finally, we offer some new characterizations of the ϕ-von Neumann regular ring.
-
Generalized derivations over amalgamated algebras along an ideal Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Brahim Boudine, Mohammed Zerra
Let A and B be two associative rings, let I be an ideal of B and let f ∈ Hom ( A , B ) {f\in\mathrm{Hom}(A,B)} . In this paper, we give a complete description of generalized derivations over A ⋈ f I {A\bowtie^{f}I} . Furthermore, when A is prime or semi-prime, we give several identities on generalized derivations which provide the commutativity of A ⋈ f I {A\bowtie^{f}I} .
-
Floquet theory and stability for a class of first order differential equations with delays Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Alexander Domoshnitsky, Elnatan Berenson, Shai Levi, Elena Litsyn
A version of the Floquet theory for first order delay differential equations is proposed. Formula of solutions representation is obtained. On this basis, the stability of first order delay differential equations is studied. An analogue of the classical integral Lyapunov–Zhukovskii test of stability is proved. New, in comparison with all known, tests of the exponential stability are obtained on the
-
Two presentations of a weak type inequality for geometric maximal operators Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Paul Hagelstein, Giorgi Oniani, Alex Stokolos
Let Φ : [ 0 , ∞ ) → [ 0 , ∞ ) {\Phi:[0,\infty)\rightarrow[0,\infty)} be a Young’s function satisfying the Δ 2 {\Delta_{2}} -condition and let M ℬ {M_{\mathcal{B}}} be the geometric maximal operator associated to a homothecy invariant basis ℬ {\mathcal{B}} acting on measurable functions on ℝ n {\mathbb{R}^{n}} . Let Q be the unit cube in ℝ n {\mathbb{R}^{n}} and let L Φ ( Q ) {L^{\Phi}(Q)} be the
-
Estimates for the commutators of Riesz transforms related to Schrödinger-type operators Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Yanhui Wang, Kang Wang
Let ℒ 2 = ( - Δ ) 2 + V 2 {\mathcal{L}_{2}=(-\Delta)^{2}+V^{2}} be the Schrödinger-type operator on ℝ n {\mathbb{R}^{n}} ( n ≥ 5 {n\geq 5} ), let H ℒ 2 1 ( ℝ n ) {H^{1}_{\mathcal{L}_{2}}(\mathbb{R}^{n})} be the Hardy space related to ℒ 2 {\mathcal{L}_{2}} , and let BMO θ ( ρ ) {\mathrm{BMO}_{\theta}(\rho)} be the BMO-type space introduced by Bongioanni, Harboure and Salinas. In this paper, we investigate
-
Some summation theorems and transformations for hypergeometric functions of Kampé de Fériet and Srivastava Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Hari M. Srivastava, Bhawna Gupta, Mohammad Idris Qureshi, Mohd Shaid Baboo
Owing to the remarkable success of the hypergeometric functions of one variable, the authors present a study of some families of hypergeometric functions of two or more variables. These functions include (for example) the Kampé de Fériet-type hypergeometric functions in two variables and Srivastava’s general hypergeometric function in three variables. The main aim of this paper is to provide several
-
A note on maximal estimate for an oscillatory operator Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Jiawei Shen, Yali Pan
We study the local maximal oscillatory integral operator T α , β ∗ ( f ) ( x ) = sup 0 < t < 1 | ∫ ℝ n e i | t ξ | α | t ξ | β Ψ ( | t ξ | ) f ^ ( ξ ) e 2 π i 〈 x , ξ 〉 𝑑 ξ | , \displaystyle T_{\alpha,\beta}^{\ast}(f)(x)=\sup_{0 0 {\beta>0} , and Ψ is a cutoff function that vanishes in a neighborhood of the origin. First, in the case 0 < p < 1 {0 1 {p>1} , which is
-
On the comparison of translation invariant convex differentiation bases Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Irakli Japaridze
It is known that if B and B ′ {B^{\prime}} are translation invariant convex density differentiation bases and the maximal operators associated to them locally majorize each other, then B and B ′ {B^{\prime}} differentiate the integrals of the same class of non-negative functions. We show that under the same conditions it is not possible to assert more about similarity of the differential properties
-
Centralizing identities involving generalized derivations in prime rings Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Vincenzo De Filippis, Pallavee Gupta, Shailesh Kumar Tiwari, Balchand Prajapati
Let ℛ {\mathcal{R}} be a prime ring of characteristic not equal to 2, let 𝒰 {\mathcal{U}} be Utumi quotient ring of ℛ {\mathcal{R}} and let 𝒞 {\mathcal{C}} be the extended centroid of ℛ {\mathcal{R}} . Let Δ be a generalized derivation on ℛ {\mathcal{R}} , and let δ 1 {\delta_{1}} and δ 2 {\delta_{2}} be derivations on ℛ {\mathcal{R}} . Let p ( v ) {p(v)} be a multilinear polynomial on ℛ {\mathcal{R}}
-
Multiplicity result for a (p(x),q(x))-Laplacian-like system with indefinite weights Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Khaled Kefi, Chaima Nefzi
Under some suitable conditions, we show that at least three weak solutions exist for a system of differential equations involving the ( p ( x ) , q ( x ) ) {(p(x),q(x))} Laplacian-like with indefinite weights. The proof is related to the Bonanno–Marano critical theorem (Appl. Anal. 89 (2010), 1–10).
-
Almost measurable functions on probability spaces Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Alexander Kharazishvili
The notion of (real-valued) almost measurable functions on probability spaces is introduced and some of their properties are considered. It is shown that any almost measurable function may be treated as a quasi-random variable in the sense of [A. Kharazishvili, On some version of random variables, Trans. A. Razmadze Math. Inst. 177 2023, 1, 143–146].
-
Numerical radii of operator matrices in terms of certain complex combinations of operators Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Cristian Conde, Fuad Kittaneh, Hamid Reza Moradi, Mohammad Sababheh
Operator matrices have played a significant role in the study of properties of the numerical radii of Hilbert space operators. This paper presents several new sharp upper bounds for the numerical radii of operator matrices in terms of certain complex combinations. The obtained results reveal many interesting properties of the numerical radius.
-
On statistical convergence of order α in partial metric spaces Georgian Math. J. (IF 0.7) Pub Date : 2024-01-01 Erdal Bayram, Çiğdem A. Bektaş, Yavuz Altın
The present study introduces the notions of statistical convergence of order α and strong p-Cesàro summability of order α in partial metric spaces. Also, we examine the inclusion relations between these concepts. In addition, we introduce the notion of λ-statistical convergence of order α in partial metric spaces while providing relations linked to these sequence spaces.
-
Existence and exponential stability of solutions for a Balakrishnan–Taylor quasilinear wave equation with strong damping and localized nonlinear damping Georgian Math. J. (IF 0.7) Pub Date : 2023-12-22 Zayd Hajjej
In the paper, we study a Balakrishnan–Taylor quasilinear wave equation | z t | α z t t - Δ z t t - ( ξ 1 + ξ 2 ∥ ∇ z ∥ 2 + σ ( ∇ z , ∇ z t ) ) Δ z - Δ z t + β ( x ) f ( z t ) + g ( z ) = 0 |z_{t}|^{\alpha}z_{tt}-\Delta z_{tt}-\bigl{(}\xi_{1}+\xi_{2}\|\nabla z\|^{2}+% \sigma(\nabla z,\nabla z_{t})\bigr{)}\Delta z-\Delta z_{t}+\beta(x)f(z_{t})+g(% z)=0 in a bounded domain
-
Concerning the Nakayama property of a module Georgian Math. J. (IF 0.7) Pub Date : 2023-12-12 Somayeh Karimzadeh, Esmaeil Rostami, Somayeh Hadjirezaei
In this paper, we thoroughly study the Nakayama property and some related concepts. Also, we describe multiplication modules that, among other things, satisfy the Nakayama property. Next, we show that a ring 𝑅 is a Max ring if and only if all modules that can be generated by a finite or countable set have the weak Nakayama property. We prove that a ring 𝑅 is a perfect ring if and only if every module
-
The Dirichlet problem in an infinite layer for a system of differential equations with shifts Georgian Math. J. (IF 0.7) Pub Date : 2023-12-12 Zinovii Nytrebych, Roman Shevchuk, Ivan Savka
In this paper, we study the problem with data on the boundary of the infinite layer { ( t , x ) : t ∈ ( 0 , h ) , x ∈ R s } , h > 0 , s ∈ N , \{(t,x):t\in(0,h),\,x\in\mathbb{R}^{s}\},\quad h>0,\,s\in\mathbb{N}, for the system of two differential equations of the second order in the time variable 𝑡 with shifts in the spatial variables x 1 , x 2 , … , x s x_{1},x_{2},\ldots,x_{s} . We propose a differential-symbol
-
A new fuzzy approach of vehicle routing problem for disaster-stricken zones Georgian Math. J. (IF 0.7) Pub Date : 2023-12-12 Gia Sirbiladze, Bezhan Ghvaberidze, Bidzina Midodashvili, Bidzina Matsaberidze, Irina Khutsishvili
Route planning problems are among the activities that have the highest impact in emergency logistical planning, goods transportation and facility location-distribution because of their effects on efficiency in resource management, service levels and client satisfaction. In the extreme conditions, such as disaster-stricken zones, the difficulty of vehicle movement between nearest different affected
-
Additivity of multiplicative (generalized) skew semi-derivations on rings Georgian Math. J. (IF 0.7) Pub Date : 2023-12-12 Sk Aziz, Arindam Ghosh, Om Prakash
In this paper, we introduce a new class of derivations that generalizes skew derivations and semi-derivations, and we call it skew semi-derivation. Furthermore, we present a study of the conditions under which this type of multiplicative derivation becomes additive.
-
Identities with generalized derivations on Lie ideals and Banach algebras Georgian Math. J. (IF 0.7) Pub Date : 2023-12-12 Abderrahman Hermas, Lahcen Oukhtite
Let 𝑅 be a prime ring and 𝐿 a non-central Lie ideal of 𝑅. In this paper, we aim to classify the generalized derivations of 𝑅 satisfying some algebraic identities with power values on 𝐿. Moreover, the same identities are studied locally on a two nonvoid open subsets of a prime Banach algebra.
-
Signless Laplacian spectrum of the cozero-divisor graph of the commutative ring ℤ𝑛 Georgian Math. J. (IF 0.7) Pub Date : 2023-12-08 Mohd Rashid, Muzibur Rahman Mozumder, Mohd Anwar
Let 𝑅 be a commutative ring with identity 1 ≠ 0 1\neq 0 and let Z ( R ) ′ Z(R)^{\prime} be the set of all non-zero and non-unit elements of ring 𝑅. Further, Γ ′ ( R ) \Gamma^{\prime}(R) denotes the cozero-divisor graph of 𝑅, is an undirected graph with vertex set Z ( R ) ′ Z(R)^{\prime} , and w ∉ z R w\notin zR and z ∉ w R z\notin wR if and only if two distinct vertices 𝑤 and 𝑧 are adjacent
-
BV capacity and perimeter in abstract Wiener spaces and applications Georgian Math. J. (IF 0.7) Pub Date : 2023-11-29 Guiyang Liu, He Wang, Yu Liu
This paper is devoted to introducing and investigating the bounded variation capacity and the perimeter in the abstract Wiener space X, thereby discovering some related inequalities. Functions of bounded variation in an abstract Wiener space X have been studied by many scholars. As the continuation of this research, we define the corresponding BV capacity cap H ( ⋅ ) {\operatorname{cap}_{H}(\,\cdot\
-
Generalized Euclidean operator radius Georgian Math. J. (IF 0.7) Pub Date : 2023-11-29 Mohammad W. Alomari, Mohammad Sababheh, Cristian Conde, Hamid Reza Moradi
In this paper, we introduce the f-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the q-operator radius. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature.
-
On a two-dimensional Dirichlet type problem for a linear hyperbolic equation of fourth order Georgian Math. J. (IF 0.7) Pub Date : 2023-11-29 Tariel Kiguradze, Reemah Alhuzally
For a linear hyperbolic equation of fourth order, a Dirichlet type boundary problem in an orthogonally convex domain is investigated. Sharp sufficient conditions guaranteeing solvability and well-posedness of the problem under consideration are established.
-
Multi-dimensional almost automorphic type sequences and applications Georgian Math. J. (IF 0.7) Pub Date : 2023-11-29 Marko Kostić, Halis Can Koyuncuoğlu
In this paper, we investigate several new classes of multi-dimensional almost automorphic type sequences and focus on their applications to various difference equations involving Volterra difference equations. We provide many structural results, illustrative examples and open problems about the notion under consideration.
-
On 〈s〉-generalized topologies Georgian Math. J. (IF 0.7) Pub Date : 2023-11-24 Jacek Hejduk, Mehmet Kucukaslan, Anna Loranty
In this paper, we focus our attention on an outer Lebesgue measure and density-type generalized topologies connected with this measure and with nondecreasing and unbounded sequences of positive reals. Some properties of such generalized topologies and continuous functions connected with this space are presented.
-
On geometrical characteristics and inequalities of new bicomplex Lebesgue Spaces with hyperbolic-valued norm Georgian Math. J. (IF 0.7) Pub Date : 2023-11-19 Erdem Toksoy, Birsen Sağır
In this work, it is assumed that the norm over bicomplex numbers is the hyperbolic ( 𝔻 {\mathbb{D}} -valued) norm. In this paper, we provide an overview of bicomplex Lebesgue spaces and investigate some of their geometric properties, including 𝔹 ℂ {\mathbb{B}\mathbb{C}} -convexity, 𝔹 ℂ {\mathbb{B}\mathbb{C}} -strict convexity, and 𝔹 ℂ {\mathbb{B}\mathbb{C}} -uniform convexity. Moreover, the
-
New quantum integral inequalities for left and right log-ℏ-convex interval-valued functions Georgian Math. J. (IF 0.7) Pub Date : 2023-11-19 Haiyang Cheng, Dafang Zhao, Guohui Zhao, Delfim F. M. Torres
We introduce the concept of quantum integration for interval-valued functions and establish new q-Hermite–Hadamard and q-Hermite–Hadamard–Fejér inequalities for left and right log - h {\mathrm{log}\text{-}h} -convex interval-valued functions. Our results generalize the known ones in the literature and serve as a foundation for future studies in inequalities for interval-valued functions and interval
-
Reproducing kernel Banach space defined by the minimal norm property and applications to partial differential equation theory Georgian Math. J. (IF 0.7) Pub Date : 2023-11-19 Tomasz Łukasz Żynda
It it well known that a Hilbert space V of functions defined on U is a reproducing kernel Hilbert space if and only if for any z ∈ U {z\in U} , in the set V z := { f ∈ V ∣ f ( z ) = 1 } {V_{z}:=\{f\in V\mid f(z)=1\}} , if non-empty, there is exactly one element with minimal norm and there is a direct connection between the reproducing kernel and such an element. In this paper, we define reproducing
-
Bilinear multipliers on weighted Orlicz spaces Georgian Math. J. (IF 0.7) Pub Date : 2023-11-19 Rüya Üster
Let Φ i {\Phi_{i}} be Young functions and ω i {\omega_{i}} be weights on ℝ d {\mathbb{R}^{d}} , i = 1 , 2 , 3 {i=1,2,3} . A locally integrable function m ( ξ , η ) {m(\xi,\eta)} on ℝ d × ℝ d {\mathbb{R}^{d}\times\mathbb{R}^{d}} is said to be a bilinear multiplier on ℝ d {\mathbb{R}^{d}} of type ( Φ 1 , ω 1 ; Φ 2 , ω 2 ; Φ 3 , ω 3 ) {(\Phi_{1},\omega_{1};\Phi_{2},\omega_{2};\Phi_{3},\omega_{3})} if
-
Fractal Mellin transform and non-local derivatives Georgian Math. J. (IF 0.7) Pub Date : 2023-11-19 Alireza Khalili Golmankhaneh, Kerri Welch, Cristina Serpa, Palle E. T. Jørgensen
This paper provides a comparison between the fractal calculus of fractal sets and fractal curves. There are introduced the analogues of the Riemann–Liouville and Caputo integrals and derivatives for fractal curves, which are non-local derivatives. Moreover, the concepts analogous to the fractional Laplace operator to address fractal non-local differential equations on fractal curves are defined. Additionally
-
On the standing wave in coupled fractional Klein–Gordon equation Georgian Math. J. (IF 0.7) Pub Date : 2023-11-19 Zhenyu Guo, Xin Zhang
The aim of this paper is to deal with the standing wave problems in coupled nonlinear fractional Klein–Gordon equations. First, we establish the constrained minimizations for a single nonlinear fractional Laplace equation. Then we prove the existence of a standing wave with a ground state using a variational argument. Next, applying the potential well argument and the concavity method, we obtain the
-
The second nonlinear mixed Lie triple derivations on standard operator algebras Georgian Math. J. (IF 0.7) Pub Date : 2023-11-19 Nadeem ur Rehman, Junaid Nisar, Bilal Ahmad Wani
Let 𝒜 {\mathcal{A}} be a standard operator algebra containing the identity operator I on an infinite dimensional complex Hilbert space ℋ {\mathcal{H}} which is closed under adjoint operation. Suppose that ϕ : 𝒜 → 𝒜 {\phi:\mathcal{A}\to\mathcal{A}} is the second nonlinear mixed Lie triple derivation. Then ϕ is an additive ∗ {\ast} -derivation.
-
Calculation of Reynolds equation for the generalized non-Newtonian fluids and its asymptotic behavior in a thin domain Georgian Math. J. (IF 0.7) Pub Date : 2023-11-19 Mohamed Dilmi, Aissa Benseghir, Mourad Dilmi, Hamid Benseridi
Three-dimensional boundary-value problem describing a generalized non-Newtonian fluid with nonlinear Tresca friction type in a thin domain Ω ε {\Omega^{\varepsilon}} are considered. We study the asymptotic behavior when one dimension of the fluid domain tends to zero. We prove some weak convergence of the velocity and the pressure of the fluid. Then the limit problem in two-dimensional domain and the
-
Existence and uniqueness of solution for the nonlinear Brusselator system with Robin boundary conditions Georgian Math. J. (IF 0.7) Pub Date : 2023-11-19 Ghassan A. Al-Juaifri, Akil J. Harfash
The system of Brusselator-type reaction-diffusion equations (RDs) on open bounded convex domains 𝒟 ⊂ ℝ d {\mathcal{D}\subset\mathbb{R}^{d}} ( d ≤ 3 ) {(d\leq 3)} with Robin boundary conditions (Rbcs) has been mathematically analyzed. The Faedo–Galerkin approach is used to demonstrate the global existence and uniqueness of a weak solution to the system. The weak solution’s higher regularity findings
-
Localization operators and inversion formulas for the Dunkl–Weinstein–Stockwell transform Georgian Math. J. (IF 0.7) Pub Date : 2023-11-07 Fethi Soltani, Ibrahim Maktouf
We define and study the Stockwell transform S g \mathscr{S}_{g} associated to the Dunkl–Weinstein operator Δ k , β \Delta_{k,\beta} and prove a Plancherel theorem and an inversion formula. Next, we define a reconstruction function f Δ f_{\Delta} and prove Calderón’s reproducing inversion formula for the Dunkl–Weinstein–Stockwell transform S g \mathscr{S}_{g} . Moreover, we define the localization operators
-
On the non-triviality of anisotropic Roumieu Gelfand–Shilov spaces and inclusion between them Georgian Math. J. (IF 0.7) Pub Date : 2023-11-02 M’Hamed Bensaid, Rachid Chaïli
The purpose of this work is to prove the non-triviality of anisotropic Roumieu Gelfand–Shilov spaces S { N } { M } ( ℝ n ) {S^{\{M\}}_{\{N\}}(\mathbb{R}^{n})} , and to establish the inclusion between them.
-
Asymptotic analysis of fundamental solutions of hypoelliptic operators Georgian Math. J. (IF 0.7) Pub Date : 2023-10-27 George Chkadua, Eugene Shargorodsky
Asymptotic behavior at infinity is investigated for fundamental solutions of a hypoelliptic partial differential operator 𝐏 ( i ∂ x ) = ( P 1 ( i ∂ x ) ) m 1 ⋯ ( P l ( i ∂ x ) ) m l \mathbf{P}(i\partial_{x})=(P_{1}(i\partial_{x}))^{m_{1}}\cdots(P_{l}(i\partial% _{x}))^{m_{l}} with the characteristic polynomial that has real multiple zeros. Based on asymptotic expansions of fundamental
-
Characterization of Hilbert C*-module higher derivations Georgian Math. J. (IF 0.7) Pub Date : 2023-10-27 S. Kh. Ekrami
Let ℳ {\mathcal{M}} be a Hilbert C * {\mathrm{C}^{*}} -module. In this paper, we show that there is a one-to-one correspondence between all Hilbert C * {\mathrm{C}^{*}} -module higher derivations { φ n : ℳ → ℳ } n = 0 ∞ {\{\varphi_{n}:\mathcal{M}\rightarrow\mathcal{M}\}_{n=0}^{\infty}} with φ 0 = I {\varphi_{0}=I} satisfying φ n ( 〈 x , y 〉 z ) = ∑ i + j + k = n 〈 φ i ( x ) , φ j ( y ) 〉 φ k ( z )
-
Study on discrete degenerate Bell distributions with two parameters Georgian Math. J. (IF 0.7) Pub Date : 2023-10-27 Taekyun Kim, Dae San Kim, Hye Kyung Kim
Recently, Freud and Rodriguez proposed a new counting process which is called the Bell–Touchard process and based on the Bell–Touchard probability distribution. This process was developed to solve the problem of rare events hypothesis which is one of the limitations of the Poisson process. In this paper, we consider the discrete degenerate Bell distributions and the degenerate Bell process which are
-
Comparison of several numerical solvers for a discretized nonlinear diffusion model with source terms Georgian Math. J. (IF 0.7) Pub Date : 2023-10-26 Beny Neta
The numerical solution of the nonlinear system of equations resulting from a real engineering problem is discussed. We use the approximate solution of a system of two nonlinear integrodifferential equations to build the nonlinear system of equations. This system can be solved by Newton’s method if the solution is differentiable, or using some derivative-free methods, such as Steffensen’s method. Here
-
On skew derivations and antiautomorphisms in prime rings Georgian Math. J. (IF 0.7) Pub Date : 2023-10-26 Amal S. Alali, Hafedh Alnoghashi, Junaid Nisar, Nadeem ur Rehman, Faez A. Alqarni
According to Posner’s second theorem, a prime ring is forced to be commutative if a nonzero centralizing derivation exists on it. In this article, we extend this result to prime rings with antiautomorphisms and nonzero skew derivations. Additionally, a case is shown to demonstrate that the restrictions placed on the theorems’ hypothesis were not unnecessary.
-
Some classes of topological spaces and the space of G-permutation degree Georgian Math. J. (IF 0.7) Pub Date : 2023-10-13 Ljubiša D. R. Kočinac, Farkhod G. Mukhamadiev, Anvar K. Sadullaev
In this paper, we study the behavior of some classes of topological spaces under the influence of the functor of G-permutation degree 𝖲𝖯 G n {\operatorname{\sf SP}^{n}_{G}} . We prove: (a) if a space X is an r-space, then so is 𝖲𝖯 G n X {\operatorname{\sf SP}_{G}^{n}X} , (b) if X is a cosmic space, then so is 𝖲𝖯 G n X {\operatorname{\sf SP}_{G}^{n}X} , (c) if a space X is a C ( κ ) {C(\kappa)}
-
On ρ-statistical convergence in neutrosophic normed spaces Georgian Math. J. (IF 0.7) Pub Date : 2023-10-03 Sibel Ersan
In this study, the concept of ρ-statistical convergence with respect to the neutrosophic norm in the neutrosophic normed spaces is introduced. Some properties and some inclusion theorems related to this concept are investigated.
-
Solution of generalized fractional kinetic equations with generalized Mathieu series Georgian Math. J. (IF 0.7) Pub Date : 2023-10-03 Mehar Chand, Özen Özer, Jyotindra C. Prajapati
We develop a new generalized form of the fractional kinetic equation involving the generalized Mathieu series. By using the Sumudu transform, a solution of these generalized fractional kinetic equation is obtained in terms of the Mittag-Leffler function. The numerical results and graphical interpretation are also presented.
-
Double lacunary statistical convergence of Δ-measurable functions on product time scales Georgian Math. J. (IF 0.7) Pub Date : 2023-10-03 Hemen Dutta, Pallav Bhattarai
We first present a notion of a double lacunary sequence on product time scales. Using this notion, we define the notions of the double lacunary statistical convergence and double lacunary strongly p-Cesàro summability of 2-multiple functions on product time scales and we study some fundamental properties of both notions. We also present a theorem that connects the above-mentioned two concepts. Furthermore