Convergence analysis for variational inequalities and fixed point problems in reflexive Banach spaces

• Main Authors: Lateef Olakunle Jolaoso, Yekini Shehu, Yeol Je Cho
• Format: Article
• Language: English
• Published: SpringerOpen 2021-03-01
• Series: Journal of Inequalities and Applications
• Subjects: Variational inequality; Fixed point; Bregman distance; Projection method; Banach spaces
• Online Access: https://doi.org/10.1186/s13660-021-02570-6

Abstract In this paper, using a Bregman distance technique, we introduce a new single projection process for approximating a common element in the set of solutions of variational inequalities involving a pseudo-monotone operator and the set of common fixed points of a finite family of Bregman quasi-nonexpansive mappings in a real reflexive Banach space. The stepsize of our algorithm is determined by a self-adaptive method, and we prove a strong convergence result under certain mild conditions. We further give some applications of our result to a generalized Nash equilibrium problem and bandwidth allocation problems. We also provide some numerical experiments to illustrate the performance of our proposed algorithm using various convex functions and compare this algorithm with other algorithms in the literature.