Fourier method in the space of φB - distributions by V. S. Mokeichev, A. M. Sidorov

“…In our previous articles, we introduced and explored the notion of φB -distributions with values in the Banach space. This offers a new perspective on the theory of solvability of linear problems, which is important for solving partial differential equations, especially equations with deviating arguments. …”
Get full text

Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator by Abdellatif Boutiara, Mohammed M. Matar, Mohammed K. A. Kaabar, Francisco Martínez, Sina Etemad, Shahram Rezapour

“…In this paper, a new class of a neutral functional delay differential equation involving the generalized ψ-Caputo derivative is investigated on a partially ordered Banach space. The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage’s technique and Banach contraction principle. …”
Get full text

Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings by Watcharaporn Cholamjiak, Suthep Suantai

“…We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. …”
Get full text

A weak ergodic theorem for infinite products of Lipschitzian mappings by Simeon Reich, Alexander J. Zaslavski

“…Let K be a bounded, closed, and convex subset of a Banach space. For a Lipschitzian self-mapping A of K, we denote by Lip(A) its Lipschitz constant. …”
Get full text

On the Characterization of a Class of Difference Equations by Muhammed Altun

“…We focus on the behavior of solutions of the difference equation 𝑥𝑛=𝑏1𝑥𝑛−1+𝑏2𝑥𝑛−2+⋯+𝑏𝑛𝑥0+𝑦𝑛, 𝑛=1,2,…, where (𝑏𝑘) is a fixed sequence of complex numbers, and (𝑦𝑘) is a fixed sequence in a complex Banach space. We give the general solution of this difference equation. …”
Get full text

A Remark on the Stability of Approximative Compactness by Zhenghua Luo, Longfa Sun, Wen Zhang

“…Let Λ be an index set and for every λ∈Λ, let Yλ be a subspace of a Banach space Xλ. For 1≤p<∞, let X=⊕lpXλ and Y=⊕lpYλ. …”
Get full text

Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions by Dongliang Yan

“…Our approach is based on the fixed-point result of Krasnoselskii type in a Banach space.…”
Get full text

Asymptotic stability of a repairable system with imperfect switching mechanism by Houbao Xu, Weihua Guo, Jingyuan Yu, Guangtian Zhu

“…We show that the system operator generates a positive C0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution. …”
Get full text

Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation by Ning Su, Li Zhang

“…We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the form d/dt𝒜u+ℬu∋ft in V′, t∈0, T, where V is a real reflexive Banach space, 𝒜 and ℬ are maximal monotone operators (possibly multivalued) from V to its dual V′. …”
Get full text

Fundamental Results about the Fractional Integro-Differential Equation Described with Caputo Derivative by Ndolane Sene

“…The existence of α-resolvent operator in Banach space and fixed point theorem has been utilized in the proof of the existence of the mild solution. …”
Get full text

On the Abstract Subordinated Exit Equation by Hassen Mejri, Ezzedine Mliki

“…Let ℙ=(𝑃𝑡)𝑡>0 be a 𝐶0-contraction semigroup on a real Banach space ℬ. A ℙ-exit law is a ℬ-valued function 𝑡∈]0,∞[→𝜑𝑡∈ℬ satisfying the functional equation: 𝑃𝑡𝜑𝑠=𝜑𝑡+𝑠, 𝑠,𝑡>0. …”
Get full text

Norm Attaining Multilinear Forms on 𝐿1(𝝁) by Yousef Saleh

“…Furthermore, the study presents an example of a Banach space 𝑋 in which the set of norm attaining operators from 𝑋 into 𝑋∗ is dense in the space of all bounded linear operators 𝐿(𝑋,𝑋∗). …”
Get full text

Four-Step <i>T</i>-Stable Generalized Iterative Technique with Improved Convergence and Various Applications by Quanita Kiran, Shaista Begum

“…The research also investigates convergence of the new iteration in uniformly convex Banach space and explores its stability. To further support our findings, we present its working on to a BV problem and to a delay DE. …”
Get full text

On the fixed points of affine nonexpansive mappings by Hülya Duru

“…Let K be a closed convex bounded subset of a Banach space X and let T:K→K be a continuous affine mapping. …”
Get full text

The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence by Linxin Li, Dingping Wu

“…Charles proved the convergence of Picard-type iteration for generalized Φ−accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ−quasi-accretive mappings and fixed points of strongly Φ−hemi-contractions, we extend the results to Noor iterative process and SP iterative process for generalized Φ−hemi-contractive mappings. …”
Get full text

Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems by Siwaporn Saewan, Poom Kumam

“…The purpose of this paper is to present a new hybrid block iterative scheme by the generalized f- projection method for finding a common element of the fixed point set for a countable family of uniformly quasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixed equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Klee property. Furthermore, we prove that our new iterative scheme converges strongly to a common element of the aforementioned sets. …”
Get full text

Iterative Scheme with Errors for Common Zeros of Finite Accretive Mappings and Nonlinear Elliptic Systems by Li Wei, Ruilin Tan

“…We present a new iterative scheme with errors to solve the problems of finding common zeros of finite m-accretive mappings in a real Banach space. Strong convergence theorems are established, which extend the corresponding works given by some authors. …”
Get full text

Strong laws of large numbers for arrays of rowwise independent random elements by Robert Lee Taylor, Tien-Chung Hu

“…Let {Xnk} be an array of rowwise independent random elements in a separable Banach space of type p+δ with EXnk=0 for all k, n. The complete convergence (and hence almost sure convergence) of n−1/p∑k=1nXnk to 0, 1≤p<2, is obtained when {Xnk} are uniformly bounded by a random variable X with E|X|2p<∞. …”
Get full text

Differentiable semigroups are Lie groups by John P. Holmes, Mitch Anderson

“…If S is a local semigroup with neighborhood of 1 homeomorphic to a Banach space and with multiplication strongly differentiable at 1, then S is a local Lie Group. …”
Get full text

The Hahn Sequence Space Defined by the Cesáro Mean by Murat Kirişci

“…The study of Hahn sequence space was initiated by Chandrasekhara Rao (1990) with certain specific purpose in the Banach space theory. In this paper, the matrix domain of the Hahn sequence space determined by the Cesáro mean first order, denoted by , is obtained, and some inclusion relations and some topological properties of this space are investigated. …”
Get full text