Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space

Abstract

We propose and analyze an inertial iterative algorithm to approximate a common solution of generalized equilibrium problem, variational inequality problem, and fixed point problem in the framework of a 2-uniformly convex and uniformly smooth real Banach space. Further, we study the convergence analysis of our proposed iterative method. Finally, we give application and a numerical example to illustrate the applicability of the main algorithm.

Hybrid Inertial Iterative Method for Fixed point, Variational Inequality and Generalized Mixed Equilibrium Problems in Banach Space

“…(1.1), V IP (1.4) and fixed point problem for a family of two quasi−φ−asymptotically nonexpansive mappings in two-uniformly convex and uniformly smooth Banach spaces. Our result extends and improves the results of Kazmi and Ali [10], Alansari et al [1] and Farid et al [6], many results in the literature.…”

“…Alansari et al [1] studied an inertial iterative method for finding a common solution of generalized equilibrium, variational inequality and fixed point problems using the sequences {x n } and {z n } generated by the iterative algorithm:…”

“…Motivated and inspired by the work of Kazmi and Ali [10], Alansari et al [1] and Farid et al [6]. We proposed a hybrid inertial iterative algorithm for approximating a common solution of GMEP.…”

An inertial iterative algorithm for generalized equilibrium problems and Bregman relatively nonexpansive mappings in Banach spaces

“…The convergence of such an algorithm has been analyzed by various researchers and illustrated its importance on data analysis and some imaging problems, see [33][34][35][36][37][38][39][40][41] for details.…”

An Inertial Iterative Algorithm to Find Common Solution of a Split Generalized Equilibrium and a Variational Inequality Problem in Hilbert Spaces

“…For further study of some generalization of iterative algorithm (8), see for instance [17,18]. Very recently, Monairah et al [19] introduced and studied a hybrid iterative algorithm to approximate a common solution of generalized equilibrium problem, variational inequality problem, and fixed point problem in the framework of a 2 uniformly convex and uniformly smooth real Banach space. e inertial method has been studied by many researchers.…”