A Modified Iterative Algorithm for Split Feasibility Problems of Right Bregman Strongly Quasi-Nonexpansive Mappings in Banach Spaces with Applications

Padcharoen, Anantachai; Kumam, Poom; Cho, Yeol; Thounthong, Phatiphat

doi:10.3390/a9040075

Volume 9, Issue 4

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Algorithms 2016, 9(4), 75; https://doi.org/10.3390/a9040075

A Modified Iterative Algorithm for Split Feasibility Problems of Right Bregman Strongly Quasi-Nonexpansive Mappings in Banach Spaces with Applications

Anantachai Padcharoen^1,2

, Poom Kumam^1,2,*

, Yeol Je Cho^3,4

and Phatiphat Thounthong^5,6

KMUTT-Fixed Point Theory and Optimization Research Group (KMUTT-FPTO), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand

KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand

Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea

⁴

Department of Mathematics, King Abdulaziz University Jeddah 21589, Saudi Arabia

⁵

Renewable Energy Research Centre, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand

⁶

Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand

Author to whom correspondence should be addressed.

Academic Editor: Alicia Cordero

Received: 8 September 2016 / Revised: 20 October 2016 / Accepted: 1 November 2016 / Published: 10 November 2016

Full-Text | PDF [459 KB, uploaded 10 November 2016] |

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Abstract

In this paper, we present a new iterative scheme for finding a common element of the solution set

F

of the split feasibility problem and the fixed point set

F (T)

of a right Bregman strongly quasi-nonexpansive mapping T in p-uniformly convex Banach spaces which are also uniformly smooth. We prove strong convergence theorem of the sequences generated by our scheme under some appropriate conditions in real p-uniformly convex and uniformly smooth Banach spaces. Furthermore, we give some examples and applications to illustrate our main results in this paper. Our results extend and improve the recent ones of some others in the literature. View Full-Text

Keywords: right Bregman strongly quasi-nonexpansive; split feasibility problem; fixed point

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Padcharoen, A.; Kumam, P.; Cho, Y.J.; Thounthong, P. A Modified Iterative Algorithm for Split Feasibility Problems of Right Bregman Strongly Quasi-Nonexpansive Mappings in Banach Spaces with Applications. Algorithms 2016, 9, 75.