Hybrid linesearch algorithm for pseudomonotone equilibrium problem and fixed points of Bregman quasi asymptotically nonexpansive multivalued mappings

Journal of Linear and Topological Algebra

دوره 10، شماره 02، شهریور 2021، صفحه 153-177   

نوع مقاله: Research Paper

نویسندگان

M. H. Harbau^{* 1}؛ B. Ali²

¹Department of Science and Technology Education‎, ‎Bayero University‎, ‎Kano‎, ‎Nigeria

²Department of Mathematical Science‎s, ‎Bayero University‎, ‎Kano‎, ‎Nigeria

چکیده

In this paper, we introduce a linesearch algorithm for solving fixed points of Bregman quasi asymptotically nonexpansive multivalued mappings and pseudomonotone equilibrium problem in reflexive Banach space. Using the linesearch method, we prove a strong convergence of the iterative scheme to a common point in the set of solutions of some equilibrium problem and common fixed point of the finite family of Bregman quasi asymptotically nonexpansive multivalued mappings with out imposing Bregman Lipschitz condition on the bifunction $g$ as used by many authors in the extragradient method. Our results improve and generalize many recent results in the literature.

کلیدواژه‌ها

Bregman-quasi-asymptotically multivalued nonexpansive mappings؛ strong convergence؛ pseudomonotone equilibrium problem؛ Legendre function

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