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J. Korean Math. Soc. 2020; 57(3): 617-640

Online first article January 9, 2020      Printed May 1, 2020

https://doi.org/10.4134/JKMS.j190268

Copyright © The Korean Mathematical Society.

A parallel iterative method for a finite family of Bregman strongly nonexpansive mappings in reflexive Banach spaces

Jong Kyu Kim, Truong Minh Tuyen

Kyungnam University; Thainguyen University of Sciences

Abstract

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In this paper, we introduce a parallel iterative method for finding a common fixed point of a finite family of Bregman strongly nonexpansive mappings in a real reflexive Banach space. Moreover, we give some applications of the main theorem for solving some related problems. Finally, some numerical examples are developed to illustrate the behavior of the new algorithms with respect to existing algorithms.

Keywords: Bregman distance, Bregman firmly nonexpansive mapping, Bregman strongly nonexpansive mapping, Bregman projection

MSC numbers: 47H05, 47H09, 47J25, 47J40, 90C25

Supported by: The first author was supported by the Basic Science Research Program through the National Research Foundation(NRF) Grant funded by Ministry of Education of the republic of Korea (2018R1D1A1B07045427) and the second author was supported by the Science and Technology Fund of ThaiNguyen University of Sciences.

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