Geodesic
Approximating Solutions of Monotone Variational Inclusion, Equilibrium and Fixed Point Problems of Certain Nonlinear Mappings in Banach Spaces
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 5, p. 777 .

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In this paper, motivated by the works of Timnak et al. [Filomat {31}(15) (2017), 4673--4693], Ogbuisi and Izuchukwu [Numer. Funct. Anal. {40}(13) (2019)] and some other related results in literature, we introduce an iterative algorithm and employ a Bregman distance approach for approximating a zero of the sum of two monotone operators, which is also a common solution of equilibrium problem involving pseudomonotone bifunction and a fixed point problem for an infinite family of Bregman quasi-nonexpansive mappings in the framework of a reflexive Banach space. Using our iterative algorithm, we state and prove a strong convergence result for approximating a common solution of the aforementioned problems. Furthermore, we give some applications of the consequences of our main result to convex minimization problem and variational inequality problem. Lastly, we display a numerical example to show the applicability of our main result. The result presented in this paper extends and complements many related results in the literature.
Classification : 47H09 47H10, 49J20
Keywords: equilibrium problem, Bregman quasi-nonexpansive, monotone operators, iterative scheme, fixed point problem 
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     title = {Approximating {Solutions} of {Monotone} {Variational} {Inclusion,} {Equilibrium} and {Fixed} {Point} {Problems} of {Certain} {Nonlinear} {Mappings} in {Banach} {Spaces}},
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Hammed Anuoluwapo Abass; Chinedu Izuchukwu; Oluwatosin Temitope Mewomo. Approximating Solutions of Monotone Variational Inclusion, Equilibrium and Fixed Point Problems of Certain Nonlinear Mappings in Banach Spaces. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 5, p. 777 . http://geodesic.mathdoc.fr/item/KJM_2023_47_5_a8/