Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces by Shenghua Wang, Shin Min Kang

“…Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. …”
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Iterative Methods for Nonconvex Equilibrium Problems in Uniformly Convex and Uniformly Smooth Banach Spaces by Messaoud Bounkhel

“…We suggest and study the convergence of some new iterative schemes for solving nonconvex equilibrium problems in Banach spaces. Many existing results have been obtained as particular cases.…”
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Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample by Chris McCarthy

“…We also present an example of a salient, closed Banach space cone C for which there does not exist a hyperplane that intersects each 0-ray in C∖{0} exactly once.…”
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Convergence for a Fixed Point of Evolution Families in Banach Space via Iterative Process by Musharaf Shah, Gul Rahmat, Syed Inayat Ali Shah, Ebenezer Bonyah, Zahir Shah, Meshal Shutaywi

“…In this paper, we present the convergence of Krasnoselskii Mann iterative process for common fixed points of pointwise Lipschitzian evolution family of bounded nonlinear operators on a Banach space ℜ.…”
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On the order of exponential growth of the solution of the linear difference equation with periodic coefficient in Banach space by H. Attia Hussein

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Higher-Order Convergent Iterative Method for Computing the Generalized Inverse over Banach Spaces by Xiaoji Liu, Fu Huang

“…A higher-order convergent iterative method is provided for calculating the generalized inverse over Banach spaces. We also use this iterative method for computing the generalized Drazin inverse in Banach algebra. …”
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The Best Approximation Theorems and Fixed Point Theorems for Discontinuous Increasing Mappings in Banach Spaces by Dezhou Kong, Lishan Liu, Yonghong Wu

“…We prove that Fan’s theorem is true for discontinuous increasing mappings f in a real partially ordered reflexive, strictly convex, and smooth Banach space X. The main tools of analysis are the variational characterizations of the generalized projection operator and order-theoretic fixed point theory. …”
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Positive Solutions for a Class of Fourth-Order Boundary Value Problems in Banach Spaces by Jingjing Cai, Guilong Liu

“…Using a specially constructed cone and the fixed point index theory, this work shows existence and nonexistence results of positive solutions for fourth-order boundary value problem with two different parameters in Banach spaces.…”
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Connections between Some Concepts of Polynomial Trichotomy for Noninvertible Evolution Operators in Banach Spaces by Mihai-Gabriel Babuţia, Nicolae Marian Seimeanu

“…The present paper treats three concepts of nonuniform polynomial trichotomies for noninvertible evolution operators acting on Banach spaces. The connections between these concepts are established through numerous examples and counterexamples for systems defined on the Banach space of square-summable sequences.…”
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An Alternative Method for the Study of Impulsive Differential Equations of Fractional Orders in a Banach Space by Asma Bouzaroura, Saïd Mazouzi

“…This paper is concerned with the existence, uniqueness, and stability of the solution of some impulsive fractional problem in a Banach space subjected to a nonlocal condition. Meanwhile, we give a new concept of a solution to impulsive fractional equations of multiorders. …”
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Fixed Point and Weak Convergence Theorems for (α,β)-Hybrid Mappings in Banach Spaces by Tian-Yuan Kuo, Jyh-Chung Jeng, Young-Ye Huang, Chung-Chien Hong

“…We introduce the class of (α,β)-hybrid mappings relative to a Bregman distance Df in a Banach space, and then we study the fixed point and weak convergence problem for such mappings.…”
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Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces by Yali Zhao, Zunquan Xia, Zeqing Liu

“…By using the notion of Jη-proximal mapping for a nonconvex, lower semicontinuous, η-subdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener-Hopf equations. …”
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Implicit Mann Type Iteration Method Involving Strictly Hemicontractive Mappings in Banach Spaces by Arif Rafiq, Shin Min Kang

“…We proved that the modified implicit Mann iteration process can be applied to approximate the fixed point of strictly hemicontractive mappings in smooth Banach spaces.…”
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Differences of Composition Operators Followed by Differentiation between Weighted Banach Spaces of Holomorphic Functions by Cui Chen, Ren-Yu Chen, Ze-Hua Zhou

“…We characterize the boundedness and compactness of differences of the composition operators followed by differentiation between weighted Banach spaces of holomorphic functions in the unit disk. …”
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A construction of a base for the M fold tensor product of a Banach space by Rohan Hemasinha

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An extension of Horn's theorem for a space of locally integrable functions by Hernan R. Henriquez, Eduardo A. Hernandez

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Solution and Stability of a Mixed Type Cubic and Quartic Functional Equation in Quasi-Banach Spaces by M. Eshaghi Gordji, S. Zolfaghari, J. M. Rassias, M. B. Savadkouhi

“…We obtain the general solution and the generalized Ulam-Hyers stability of the mixed type cubic and quartic functional equation f(x+2y)+f(x−2y)=4(f(x+y)+f(x−y))−24f(y)−6f(x)+3f(2y) in quasi-Banach spaces.…”
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An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces by Huijuan Jia, Shufen Liu, Yazheng Dang

“…In this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern’s iteration with an inertial technique for the problem. …”
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Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces by Aunyarat Bunyawat, Suthep Suantai

“…We introduce an iterative method for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mapping {Ti} in a uniformly convex Banach space. We prove that under certain control conditions, the iterative sequence generated by our method is an approximating fixed point sequence of each Ti. …”
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On Sums of Strictly Narrow Operators Acting from a Riesz Space to a Banach Space by Oleksandr Maslyuchenko, Mikhail Popov

“…We prove that if E is a Dedekind complete atomless Riesz space and X is a Banach space, then the sum of two laterally continuous orthogonally additive operators from E to X, one of which is strictly narrow and the other one is hereditarily strictly narrow with finite variation (in particular, has finite rank), is strictly narrow. …”
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