Approximating Fixed Points of Bregman Generalized ? -Nonexpansive Mappings

Kanikar Muangchoo, Poom Kumam, Yeol Je Cho, Sompong Dhompongsa and Sakulbuth Ekvittayaniphon
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Kanikar Muangchoo: KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
Poom Kumam: KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
Yeol Je Cho: Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
Sompong Dhompongsa: KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
Sakulbuth Ekvittayaniphon: Rajamangala University of Technology Phra Nakhon, 399 Samsen Rd., Vachira Phayaban, Dusit, Bangkok 10300, Thailand

Mathematics, 2019, vol. 7, issue 8, 1-28

Abstract: In this paper, we introduce a new class of Bregman generalized α -nonexpansive mappings in terms of the Bregman distance. We establish several weak and strong convergence theorems of the Ishikawa and Noor iterative schemes for Bregman generalized α -nonexpansive mappings in Banach spaces. A numerical example is given to illustrate the main results of fixed point approximation using Halpern’s algorithm.

Keywords: fixed point; Bregman distance; Bregman function; Bregman–Opial property; generalized ?-nonexpansive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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