Metric Characterizations of α-Well-Posedness for a System of Mixed Quasivariational-Like Inequalities in Banach Spaces by L. C. Ceng, Y. C. Lin

“…The purpose of this paper is to investigate the problems of the well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept of α-well-posedness to the system of mixed quasivariational-like inequalities, which includes symmetric quasi-equilibrium problems as a special case. …”
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Lebesgue's Differentiation Theorems in R.I. Quasi-Banach Spaces and Lorentz Spaces Γp,w by Maciej Ciesielski, Anna Kamińska

“…The paper is devoted to investigation of new Lebesgue's type differentiation theorems (LDT) in rearrangement invariant (r.i.) quasi-Banach spaces E and in particular on Lorentz spaces Γp,w={f:∫(f**)pw<∞} for any 0<p<∞ and a nonnegative locally integrable weight function w, where f** is a maximal function of the decreasing rearrangement f* for any measurable function f on (0,α), with 0<α≤∞. …”
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Proximal Point Algorithms for Finding a Zero of a Finite Sum of Monotone Mappings in Banach Spaces by H. Zegeye, N. Shahzad

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Extragradient Methods for Solving Split Feasibility Problem and General Equilibrium Problem and Resolvent Operators in Banach Spaces by Mostafa Ghadampour

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Some Random Fixed-Point Theorems for Weakly Contractive Random Operators in a Separable Banach Space by Kenza Benkirane, Abderrahim EL Adraoui, El Miloudi Marhrani

“…The aim of this paper is to prove a common random fixed-point and some random fixed-point theorems for random weakly contractive operators in separable Banach spaces. A random Mann iterative process is introduced to approximate the fixed point. …”
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Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces by Yekini Shehu, Jerry N. Ezeora

“…Let E be a real Banach space which is uniformly smooth and uniformly convex. …”
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Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞-Uniformly Smooth and Strictly Convex Banach Spaces by Meng Wen, Changsong Hu, Zhiyu Wu

“…We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in 𝑞-uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. …”
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A Novel Picture Fuzzy n-Banach Space with Some New Contractive Conditions and Their Fixed Point Results by Awais Asif, Hassen Aydi, Muhammad Arshad, Zeeshan Ali

“…By using these contractive conditions, we explore some fixed point theorems in a picture fuzzy n-Banach space (BPF). The discussed modified results are more general than those in the existing literature which are based on an intuitionistic fuzzy n-Banach space (BIF) and a fuzzy n-Banach space. …”
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Convergence Theorems for a Maximal Monotone Operator and a 𝑉-Strongly Nonexpansive Mapping in a Banach Space by Hiroko Manaka

“…Let E be a smooth Banach space with a norm ‖⋅‖. Let 𝑉(𝑥,𝑦)=‖𝑥‖2+‖𝑦‖2−2⟨𝑥,𝐽𝑦⟩ for any 𝑥,𝑦∈𝐸, where ⟨⋅,⋅⟩ stands for the duality pair and J is the normalized duality mapping. …”
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Convergence Theorems on a New Iteration Process for Two Asymptotically Nonexpansive Nonself-Mappings with Errors in Banach Spaces by Murat Ozdemir, Sezgin Akbulut, Hukmi Kiziltunc

“…We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. …”
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Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space by Bo Liu, Yansheng Liu

“…This paper investigates the existence of positive solutions to a two-point boundary value problem (BVP) for singular fractional differential equations in Banach space and presents a number of new results. First, by constructing a novel cone and using the fixed point index theory, a sufficient condition is established for the existence of at least two positive solutions to the approximate problem of the considered singular BVP. …”
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Ulam Stability and Non-Stability of Additive Functional Equation in IFN-Spaces and 2-Banach Spaces by Different Methods by N. Uthirasamy, K. Tamilvanan, Masho Jima Kabeto

“…The main goal of this study is to examine the Ulam stability of this equation in IFN-spaces (intuitionistic fuzzy normed spaces) with the help of direct and fixed point approaches and 2-Banach spaces. Also, we use an appropriate counterexample to demonstrate that the stability of this equation fails in a particular case.…”
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Hybrid Implicit Iteration Process for a Finite Family of Non-Self-Nonexpansive Mappings in Uniformly Convex Banach Spaces by Qiaohong Jiang, Jinghai Wang, Jianhua Huang

“…Weak and strong convergence theorems are established for hybrid implicit iteration for a finite family of non-self-nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results.…”
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Strong Convergence of Iterative Algorithm for a New System of Generalized H·,·-η-Cocoercive Operator Inclusions in Banach Spaces by Saud M. Alsulami, Eskandar Naraghirad, Nawab Hussain

“…We introduce and study a new system of generalized H·,·-η-cocoercive operator inclusions in Banach spaces. Using the resolvent operator technique associated with H·,·-η-cocoercive operators, we suggest and analyze a new generalized algorithm of nonlinear set-valued variational inclusions and establish strong convergence of iterative sequences produced by the method. …”
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Approximately Quintic and Sextic Mappings Form r-Divisible Groups into Ŝerstnev Probabilistic Banach Spaces: Fixed Point Method by M. Eshaghi Gordji, Y. J. Cho, M. B. Ghaemi, H. Majani

“…Using the fixed point method, we investigate the stability of the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients form r-divisible groups into Ŝerstnev probabilistic Banach spaces.…”
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Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces by Prasit Cholamjiak, Suthep Suantai

“…In addition, the results obtained in this paper can be applied to a system of variational inequality problems and to a system of convex minimization problems in a Banach space.…”
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Quartic Functional Equation: Ulam-Type Stability in β,p-Banach Space and Non-Archimedean β-Normed Space by Ravinder Kumar Sharma, Sumit Chandok

“…In this study, we use the alternative fixed-point approach and the direct method to examine the generalized Hyers–Ulam stability of the quartic functional equation  gu+mv+gu−mv=2m−17m−9gu+2m2−1m2gv−m−12g2u+m2gu+v+gu−v, with a fixed positive integer m/ge2 in the context of β,p-Banach space. In non-Archimedean β-normed space, we also verify Hyers–Ulam stability for the quartic functional equation stated. …”
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A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces by Pongsakorn Sunthrayuth, Poom Kumam

“…We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. …”
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Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability by Manuel De la Sen, Asier Ibeas

“…This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. …”
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Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space by Wariam Chuayjan, Sornsak Thianwan

“…Using this result, we obtain some applications in a Banach space. The results obtained in this paper extend and improve the several recent results in this area.…”
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