A hybrid iteration for asymptotically strictly pseudocontractive mappings

The purpose of this paper is to propose an algorithm for solvingthe split common fixed point problems for total asymptotically strictly pseudocontractive mappingsin infinite-dimensional Hilbert spaces. The results presented in the paper improve and extend some recent results of Moudafi (2011 and 2010), Xu (2010 and 2006), Censor and Segal (2009), Censor et al. (2005), Masad and Reich (2007), Censor et al. (2007), Yang (2004), and others.

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Explicit averaging cyclic algorithm for common fixed points of a finite family of asymptotically strictly pseudocontractive mappings in q-uniformly smooth Banach spaces

Fixed Point Theory and Applications ◽

10.1186/1687-1812-2012-167 ◽

2012 ◽

Vol 2012 (1) ◽

Author(s):

Ying Zhang ◽

Zhiwei Xie

Keyword(s):

Fixed Points ◽

Banach Spaces ◽

Common Fixed Points ◽

Finite Family ◽

Pseudocontractive Mappings ◽

Uniformly Smooth ◽

Cyclic Algorithm ◽

Uniformly Smooth Banach Spaces ◽

Asymptotically Strictly Pseudocontractive Mappings ◽

Strictly Pseudocontractive Mappings

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An approximate solution to the fixed point problems for an infinite family of asymptotically strictly pseudocontractive mappings in the intermediate sense, cocoercive quasivariational inclusions problems and mixed equilibrium problems in Hilbert spaces

Fixed Point Theory and Applications ◽

10.1186/1687-1812-2012-214 ◽

2012 ◽

Vol 2012 (1) ◽

Author(s):

Pattanapong Tianchai

Keyword(s):

Fixed Point ◽

Approximate Solution ◽

Hilbert Spaces ◽

Equilibrium Problems ◽

Infinite Family ◽

Pseudocontractive Mappings ◽

Mixed Equilibrium Problems ◽

Quasivariational Inclusions ◽

Asymptotically Strictly Pseudocontractive Mappings ◽

Strictly Pseudocontractive Mappings

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The split equality fixed-point problem for totally quasi-asymptotically strictly pseudocontractive mappings without prior knowledge of operator norms

Journal of Nonlinear Functional Analysis ◽

10.23952/jnfa.2019.43 ◽

2019 ◽

Vol 2019 (1) ◽

Keyword(s):

Fixed Point ◽

Prior Knowledge ◽

Fixed Point Problem ◽

Point Problem ◽

Pseudocontractive Mappings ◽

Operator Norms ◽

Asymptotically Strictly Pseudocontractive Mappings ◽

Strictly Pseudocontractive Mappings

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Parallel hybrid methods for generalized equilibrium problems and asymptotically strictly pseudocontractive mappings

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-015-0980-9 ◽

2016 ◽

Vol 53 (1-2) ◽

pp. 531-554 ◽

Cited By ~ 12

Author(s):

Dang Van Hieu

Keyword(s):

Equilibrium Problems ◽

Hybrid Methods ◽

Pseudocontractive Mappings ◽

Parallel Hybrid ◽

Generalized Equilibrium ◽

Asymptotically Strictly Pseudocontractive Mappings ◽

Strictly Pseudocontractive Mappings

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The Split Common Fixed Point Problem for a Family of Multivalued Quasinonexpansive Mappings and Totally Asymptotically Strictly Pseudocontractive Mappings in Banach Spaces

Mathematics ◽

10.3390/math5010011 ◽

2017 ◽

Vol 5 (1) ◽

pp. 11 ◽

Cited By ~ 1

Author(s):

Ali Abkar ◽

Elahe Shahrosvand ◽

Azizollah Azizi

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Banach Spaces ◽

Fixed Point Problem ◽

Point Problem ◽

Pseudocontractive Mappings ◽

Common Fixed Point Problem ◽

Split Common Fixed Point ◽

Asymptotically Strictly Pseudocontractive Mappings ◽

Strictly Pseudocontractive Mappings

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Convergence rate estimate of ishikawa iterative sequence for strictly pseudocontractive mappings

Applied Mathematics-A Journal of Chinese Universities ◽

10.1007/s11766-002-0044-4 ◽

2002 ◽

Vol 17 (2) ◽

pp. 189-192

Author(s):

Luchuan Zeng

Keyword(s):

Convergence Rate ◽

Iterative Sequence ◽

Rate Estimate ◽

Convergence Rate Estimate ◽

Pseudocontractive Mappings ◽

Ishikawa Iterative Sequence ◽

Strictly Pseudocontractive Mappings

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A New Hybrid Iterative Method for Solving a Mixed Equilibrium Problem and a Fixed Point Problem for Quasi-Bregman Strictly Pseudocontractive Mappings

Data Science for Financial Econometrics - Studies in Computational Intelligence ◽

10.1007/978-3-030-48853-6_30 ◽

2020 ◽

pp. 417-444

Author(s):

Kanikar Muangchoo ◽

Poom Kumam ◽

Yeol Je Cho ◽

Sakulbuth Ekvittayaniphon

Keyword(s):

Fixed Point ◽

Iterative Method ◽

Equilibrium Problem ◽

Fixed Point Problem ◽

Point Problem ◽

Mixed Equilibrium Problem ◽

Pseudocontractive Mappings ◽

Mixed Equilibrium ◽

Hybrid Iterative Method ◽

Strictly Pseudocontractive Mappings

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Split equality fixed point problem for strictly pseudocontractive mappings

International Mathematical Forum ◽

10.12988/imf.2014.410176 ◽

2014 ◽

Vol 9 ◽

pp. 1707-1718

Author(s):

Zhaoli Ma ◽

Wen Duan ◽

RuiJuan Liu

Keyword(s):

Fixed Point ◽

Fixed Point Problem ◽

Point Problem ◽

Pseudocontractive Mappings ◽

Strictly Pseudocontractive Mappings

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Convergence Theorems for Fixed Points of Multivalued Strictly Pseudocontractive Mappings in Hilbert Spaces

Abstract and Applied Analysis ◽

10.1155/2013/629468 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 13

Author(s):

C. E. Chidume ◽

C. O. Chidume ◽

N. Djitté ◽

M. S. Minjibir

Keyword(s):

Hilbert Space ◽

Fixed Point ◽

Hilbert Spaces ◽

Convex Subset ◽

Real Hilbert Space ◽

Convergence Theorems ◽

Strictly Pseudocontractive Mapping ◽

Pseudocontractive Mappings ◽

Iteration Sequence ◽

Strictly Pseudocontractive Mappings

LetKbe a nonempty, closed, and convex subset of a real Hilbert spaceH. Suppose thatT:K→2Kis a multivalued strictly pseudocontractive mapping such thatF(T)≠∅. A Krasnoselskii-type iteration sequence{xn}is constructed and shown to be an approximate fixed point sequence ofT; that is,limn→∞d(xn,Txn)=0holds. Convergence theorems are also proved under appropriate additional conditions.

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