On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
Prondanai Kaskasem ◽  
Chakkrid Klin-eam ◽  
Suthep Suantai
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces

scholarly journals Characterizations of fixed points of nonexpansive mappings

2005 ◽  
Vol 2005 (11) ◽  
pp. 1723-1735 ◽  
Author(s):  
Tomonari Suzuki
Keyword(s):  
Banach Space ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Strict Convexity ◽  
Banach Limit ◽  
Banach Limits

Using the notion of Banach limits, we discuss the characterization of fixed points of nonexpansive mappings in Banach spaces. Indeed, we prove that the two sets of fixed points of a nonexpansive mapping and some mapping generated by a Banach limit coincide. In our discussion, we may not assume the strict convexity of the Banach space.

scholarly journals Some Results on the Approximation of Solutions of Variational Inequalities for Multivalued Maps on Banach Spaces

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Luigi Muglia ◽  
Giuseppe Marino
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces ◽  
Unique Solution ◽  
Nonexpansive Mappings ◽  
Multivalued Maps ◽  
Demiclosedness Principle

AbstractMultivalued $$*$$ ∗ -nonexpansive mappings are studied in Banach spaces. The demiclosedness principle is established. Here we focus on the problem of solving a variational inequality which is defined on the set of fixed points of a multivalued $$*$$ ∗ -nonexpansive mapping. For this purpose, we introduce two algorithms approximating the unique solution of the variational inequality.

scholarly journals Approximation of Fixed Points of Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-23 ◽  
Author(s):  
Jiawei Chen ◽  
Zhongping Wan ◽  
Liuyang Yuan ◽  
Yue Zheng
Keyword(s):  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Relatively Nonexpansive Mapping ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive ◽  
Projection Techniques

We introduce a concept of weak Bregman relatively nonexpansive mapping which is distinct from Bregman relatively nonexpansive mapping. By using projection techniques, we construct several modification of Mann type iterative algorithms with errors and Halpern-type iterative algorithms with errors to find fixed points of weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpansive mappings in Banach spaces. The strong convergence theorems for weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpansive mappings are derived under some suitable assumptions. The main results in this paper develop, extend, and improve the corresponding results of Matsushita and Takahashi (2005) and Qin and Su (2007).

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