Iterative Schemes for Nonconvex Quasi-Variational Problems with V-Prox-Regular Data in Banach Spaces by M. Bounkhel, Dj. Bounekhel

“…We study the convergence of some algorithms to solutions of the proposed nonconvex problems in Banach spaces.…”
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Iterative solutions of K-positive definite operator equations in real uniformly smooth Banach spaces by Zeqing Liu, Shin Min Kang, Jeong Sheok Ume

“…Let X be a real uniformly smooth Banach space and let T:D(T)⫅X→X be a K-positive definite operator. …”
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Existence of Solutions for Fractional Integro-Differential Equation with Multipoint Boundary Value Problem in Banach Spaces by Yulin Zhao, Li Huang, Xuebin Wang, Xianyang Zhu

“…By means of the fixed-point theorem in the cone of strict-set-contraction operators, we consider the existence of a nonlinear multi-point boundary value problem of fractional integro-differential equation in a Banach space. In addition, an example to illustrate the main results is given.…”
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New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces by Rabian Wangkeeree, Pakkapon Preechasilp

“…The strong convergence theorem of the proposed sequence is obtained in a Banach space setting. The main results extend various results existing in the current literature.…”
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The Solution by Iteration of a Composed K-Positive Definite Operator Equation in a Banach Space by S. J. Aneke

“…The equation 𝐿𝑢=𝑓, where 𝐿=𝐴+𝐵, with 𝐴 being a K-positive definite operator and 𝐵 being a linear operator, is solved in a Banach space. Our scheme provides a generalization to the so-called method of moments studied in a Hilbert space by Petryshyn (1962), as well as Lax and Milgram (1954). …”
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Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces

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An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces by H. Zegeye, N. Shahzad

“…We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for a monotone mapping and fixed point of uniformly Lipschitzian relatively asymptotically nonexpansive mapping in Banach spaces. As a consequence, we provide a scheme that converges strongly to a common zero of finite family of monotone mappings under suitable conditions. …”
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Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces by Liang Chen, Chuanqing Gu, Yanfang Ma

“…We study a modified Newton's method with fifth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations. …”
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Essential Norms of Stević–Sharma Operators from General Banach Spaces into Zygmund-Type Spaces by M. A. Bakhit

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Weak and Strong Convergence Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings in Banach Spaces by Lei Deng, Juan Xiao

“…A finite-step iteration sequence for two finite families of asymptotically nonexpansive mappings is introduced and the weak and strong convergence theorems are proved in Banach space. The results presented in the paper generalize and unify some important known results of relevant scholars.…”
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Multiple Solutions for Boundary Value Problems of th-Order Nonlinear Integrodifferential Equations in Banach Spaces by Yanlai Chen

“…The boundary value problems of a class of th-order nonlinear integrodifferential equations of mixed type in Banach space are considered, and the existence of three solutions is obtained by using the fixed-point index theory.…”
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Strong Convergence Theorems for Mixed Equilibrium Problem and Asymptotically I-Nonexpansive Mapping in Banach Spaces by Bin-Chao Deng, Tong Chen, Yi-Lin Yin

“…This paper aims to use a hybrid algorithm for finding a common element of a fixed point problem for a finite family of asymptotically nonexpansive mappings and the set solutions of mixed equilibrium problem in uniformly smooth and uniformly convex Banach space. Then, we prove some strong convergence theorems of the proposed hybrid algorithm to a common element of the above two sets under some suitable conditions.…”
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Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces by He Yang

“…This paper deals with the existence and uniqueness of mild solutions for the initial value problems of abstract impulsive evolution equations in an ordered Banach space E:u′(t)+Au(t)=f(t,u(t),Gu(t)), t∈[0,a], t≠tk, Δu|t=tk=Ik(u(tk)), 0<t1<t2<⋯<tm<a, u(0)=u0, where A:D(A)⊂E→E is a closed linear operator, and f:[0,a]×E×E→E is a nonlinear mapping. …”
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Convergence of weighted sums of independent random variables and an extension to Banach space-valued random variables by W. J. Padgett, R. L. Taylor

Subjects: “…random elements in Banach space…”
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Existence Results for a Class of Semilinear Fractional Partial Differential Equations with Delay in Banach Spaces by Bo Zhu, Baoyan Han, Xiangyun Lin

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On the Hyers-Ulam Stability of a General Mixed Additive and Cubic Functional Equation in n-Banach Spaces by Tian Zhou Xu, John Michael Rassias

“…The objective of the present paper is to determine the generalized Hyers-Ulam stability of the mixed additive-cubic functional equation in n-Banach spaces by the direct method. In addition, we show under some suitable conditions that an approximately mixed additive-cubic function can be approximated by a mixed additive and cubic mapping.…”
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Nonlinear Impulsive Differential Equations with Weighted Exponential or Ordinary Dichotomous Linear Part in a Banach Space by Hristo Kiskinov, Andrey Zahariev

“…We consider nonlinear impulsive differential equations with ψ-exponential and ψ-ordinary dichotomous linear part in a Banach space. By the help of Banach’s fixed-point principle sufficient conditions are found for the existence of ψ-bounded solutions of these equations on R and R+.…”
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Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces by Chin-Tzong Pang, Eskandar Naraghirad

“…We introduce a general algorithm to approximate common fixed points for a countable family of nonexpansive mappings in a real Banach space. We prove strong convergence theorems for the sequences produced by the methods and approximate a common fixed point of a countable family of nonexpansive mappings which solves uniquely the corresponding variational inequality. …”
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Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach Spaces by Yan Tang

“…Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. …”
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A New Hybrid Algorithm for λ-Strict Asymptotically Pseudocontractions in 2-Uniformly Smooth Banach Spaces by Xin-dong Liu, Shih-sen Chang

“…Using the metric projection, a strong convergence theorem is obtained in a uniformly convex and 2-uniformly smooth Banach spaces. The result presented in this paper mainly improves and extends the corresponding results of Matsushita and Takahashi (2008), Dehghan (2011) Kang and Wang (2011), and many others.…”
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