1. Locating common fixed points of nonlinear representations of semigroups
- Author
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Kyung Soo Kim, Jen-Chih Yao, Hong-Yi Chen, Ngai-Ching Wong, Ching-Feng Wen, and Eskandar Naraghirad
- Subjects
Pure mathematics ,Semigroup ,General Mathematics ,010102 general mathematics ,Fixed point ,Type (model theory) ,Bregman divergence ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Scheme (mathematics) ,Convergence (routing) ,0101 mathematics ,Representation (mathematics) ,Mathematics - Abstract
This paper is concerned with the problem of finding common fixed points for a family of Bregman relatively weak nonexpansive mappings. The motivation is due to our finding of some gaps in a paper of K. S. Kim (Nonlinear Analysis, 73 (2010), 3413-3419), where the author was developing a hybrid iterative scheme for locating common fixed points of a nonlinear representation of a left reversible semigroup. After a brief discussion about the gaps and why they are fatal, we present a new approach by using Bergman type nonexpansive mappings. A correct version of Kim’s convergence theorem is given as a consequence of our new results, which also improve and extend some recent results in the literature.
- Published
- 2019