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- Title
APPROXIMATING SOLUTIONS OF MONOTONE VARIATIONAL INCLUSION, EQUILIBRIUM AND FIXED POINT PROBLEMS OF CERTAIN NONLINEAR MAPPINGS IN BANACH SPACES.
- Authors
ABASS, HAMMED ANUOLUWAPO; IZUCHUKWU, CHINEDU; MEWOMO, OLUWATOSIN TEMITOPE
- Abstract
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.
- Subjects
MONOTONE operators; BANACH spaces; NONLINEAR equations; EQUILIBRIUM
- Publication
Kragujevac Journal of Mathematics, 2023, Vol 47, Issue 5, p777
- ISSN
1450-9628
- Publication type
Article
- DOI
10.46793/KgJMat2305.777A