Inertial iterative method for solving generalized equilibrium, variational inequality, and fixed point problems of multivalued mappings in Banach space

Abstract

Abstract We devise an iterative algorithm incorporating inertial techniques to approximate the shared solution of a generalized equilibrium problem, a fixed point problem for a finite family of relatively nonexpansive multivalued mappings, and a variational inequality problem. Our discussion encompasses the strong convergence of the proposed algorithm and highlights specific outcomes derived from our theorem. Additionally, we provide a computational analysis to underscore the significance of our findings and draw comparisons. The results presented in this paper serve to extend and unify numerous previously established outcomes in this particular research domain.

Keywords

• Generalized equilibrium problem
• Variational inequality problem
• Relatively nonexpansive multivalued mapping
• Iterative methods
• Fixed point problem