Results 71 to 80 of about 4,652 (229)
On directionally nonexpansive mappings
European Journal of MathematicsAbstractIn 2000, W.A. Kirk introduced the concept of directionally nonexpansive mappings. Here, we present a more comprehensive study of this class of mappings, including a fixed-point result for them. We further present a class of mappings, properly containing the directionally nonexpansive ones, for which Kirk’s theorem still holds.
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Journal of Mathematics, Volume 2025, Issue 1, 2025.In this paper, our goal is to prove the existence of a weak solution (in H01Ω) for a fully nonlinear Dirichlet problem with a nonmonotone (e.g., Lipschitz) convection function F that depends on ∇u, and a nonlinearity G that is not necessarily monotone and depends on the solution function u, and the higher order term is −ΔΓ(x, u) − diva(x, u, ∇u ...
Teffera M. Asfaw +3 more
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Convergences of Weighted Averaged Operators in p‐Uniformly Convex Metric Spaces
Journal of Mathematics, Volume 2025, Issue 1, 2025.This paper presents improvements to theorems concerning the △‐convergence of iterative sequences in p‐uniformly convex metric spaces. The analysis focuses on sequences generated by weighted average operators applied to pairs of simultaneous quasi‐nonexpansive mappings.
Anawat Rodchan +2 more
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Strong convergence theorems for a sequence of nonexpansive mappings with gauge functions
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013 In this paper, we first prove a path convergence theorem for a nonexpansive mapping in a reflexive and strictly convex Banach space which has a uniformly Gˆateaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function on [0,∞).
Cholamjiak Prasit +2 more
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Two‐Step Inertial Algorithms for Nonexpansive Mappings: An Application to Osteoporosis
Journal of Mathematics, Volume 2025, Issue 1, 2025.This paper introduces a novel approach incorporating a double inertial technique with Mann’s algorithm to find common fixed points of two nonexpansive mappings. We rigorously prove the weak convergence of this algorithm under suitable conditions. The applications section explores the connection among nonexpansive mappings, split equilibrium problems ...
Watcharapon Yajai +4 more
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Neural‐network‐based regularization methods for inverse problems in imaging
GAMM-Mitteilungen, Volume 47, Issue 4, November 2024.Abstract This review provides an introduction to—and overview of—the current state of the art in neural‐network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied mathematics and a basic understanding of neural networks to different concepts of applying neural networks for ...
Andreas Habring, Martin Holler
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Journal of Applied Mathematics, 2012 We introduce a new regularization iterative algorithm for equilibrium and fixed point problems of nonexpansive mapping. Then, we prove a strong convergence theorem for nonexpansive mappings to solve a unique solution of the variational inequality and the
Shuo Sun
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Abstract and Applied Analysis, 2010 Let E be a real Banach space which is uniformly smooth and uniformly convex. Let K be a nonempty, closed, and convex sunny nonexpansive retract of E, where Q is the sunny nonexpansive retraction. If E admits weakly sequentially continuous duality mapping
Yekini Shehu, Jerry N. Ezeora
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Fixed point theorems for nonexpansive mappings [PDF]
Pacific Journal of Mathematics, 1972 The notions of nonexpansive, contractive, iteratively contractive and strictly contractive mappings have been generalized to a Hausdorff topological space whose topology is generated by a family of pseudometries . A fixed point theorem for strictly contractive mappings is obtained which generalizes the Banach's contractive mapping principle.
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Journal of Function Spaces, 2019 In this paper, we introduce a new accelerated iteration for finding a fixed point of monotone generalized α-nonexpansive mapping in an ordered Banach space.
Yi-An Chen, Dao-Jun Wen
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