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Iterative Algorithms for Nonexpansive Mappings [PDF]

Fixed Point Theory and Applications, 2008
AbstractWe suggest and analyze two new iterative algorithms for a nonexpansive mapping T in Banach spaces. We prove that the proposed iterative algorithms converge strongly to some fixed point of T.
Yonghong Yao, Liou Yeong-Cheng
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Convergence analysis of Suzuki's generalized nonexpansive mappings using the Picard-Abbas iteration process. [PDF]

PLoS One
Nawaz B, Gdawiec K, Ullah K, Noorwali M, Aphane M.   +4 more
europepmc   +2 more sources

Iterated nonexpansive mappings [PDF]

Journal of Fixed Point Theory and Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tomás Domínguez Benavides, Enrique Llorens-Fuster   +1 more
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Fixed points of weakly K-nonexpansive mappings and a stability result for fixed point iterative process with an application

Journal of Inequalities and Applications, 2022
In this article, we introduce a new type of non-expansive mapping, namely weakly K-nonexpansive mapping, which is weaker than non-expansiveness and stronger than quasi-nonexpansiveness.
Sayantan Panja, Kushal Roy, Marija V. Paunović, Mantu Saha, Vahid Parvaneh   +4 more
doaj   +1 more source

Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems

Journal of Mathematics, 2021
In this article, we introduce cyclic relatively nonexpansive mappings with respect to orbits and prove that every cyclic relatively nonexpansive mapping with respect to orbits T satisfying TA⊆B,TB⊆A has a best proximity point.
Laishram Shanjit, Yumnam Rohen, K. Anthony Singh   +2 more
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A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings

Journal of Inequalities and Applications, 2009
A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of ...
Klin-eam Chakkrid, Suantai Suthep
doaj   +2 more sources

A Modified Proximal Point Algorithm and Some Convergence Results

Journal of Mathematics, 2021
In this paper, the convergence to minimizers of a convex function of a modified proximal point algorithm involving a single-valued nonexpansive mapping and a multivalued nonexpansive mapping in CAT(0) spaces is studied and a numerical example is given to
Shengquan Weng, Dingping Wu, Zengfu Chao
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Convergence theorems for total asymptotically nonexpansive mappings in CAT ( κ ) $\operatorname{CAT} (\kappa )$ spaces

Fixed Point Theory and Algorithms for Sciences and Engineering, 2023
The purpose of this paper is to study the convergence theorems in CAT ( κ ) $\operatorname{CAT} (\kappa )$ spaces with k > 0 $k > 0$ for total asymptotically nonexpansive mappings which are essentially wider than nonexpansive mappings, asymptotically ...
Shih-sen Chang, Liangcai Zhao, Min Liu, Jinfang Tang   +3 more
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On Nonexpansive Mappings [PDF]

Proceedings of the American Mathematical Society, 1964
holds for all p, qEX (for all p, q with d(p, q)
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On Nonexpansive Mappings [PDF]

Proceedings of the American Mathematical Society, 1976
A generalized Hilbert space property is used to analyze nonexpansive mappings in certain settings. In particular it is shown that in l 1 {l_1} and in the important, recently defined, space J 0 {J_0} , a nonexpansive self-mapping of a bounded weak
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