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Demiclosedness Principles for Generalized Nonexpansive Mappings [PDF]
Journal of Optimization Theory and Applications, 2020 Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments for the weak convergence of the shadow sequence generated by the Douglas-Rachford algorithm. We provide extensions
Sedi Bartz, Rubén Campoy, Hung M. Phan
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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 +4 more
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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 +2 more
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Iterative Algorithms for Nonexpansive Mappings [PDF]
Fixed Point Theory and Applications, 2007 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.
Yao Yonghong, Liou Yeong-Cheng
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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
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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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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 +3 more
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ORBITALLY NONEXPANSIVE MAPPINGS [PDF]
Bulletin of the Australian Mathematical Society, 2015 We define a class of nonlinear mappings which is properly larger than the class of nonexpansive mappings. We also give a fixed point theorem for this new class of mappings.
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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
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Strong Convergence Theorems for Nonexpansive Mapping [PDF]
Journal of Systems Science and Complexity, 2007 Let \(C\) be a closed convex subset of a uniformly smooth Banach space \(E\) and \(T\) a nonexpansive selfmap of \(C\) with \(F(T) \neq \emptyset\). Given a point \(u \in C\) and an initial guess \(x_0 \in C\), the author proves the strong convergence of the iteration scheme defined by \(z_n = \gamma_nx_n + (1 - \gamma_n)Tx_n\), \(y_n = \beta_nx_n + (1
Yongfu Su, Xiaolong Qin
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