An extragradient algorithm for split generalized equilibrium problem and the set of fixed points ofquasi-$\phi $-nonexpansive mappings in Banach spaces

Authors

Olawale Oyewole
OLUWATOSIN MEWOMO
LATEEF JOLAOSO
Safeer Hussain KHAN

DOI

10.3906/mat-1911-83

Abstract

In this paper, we study the problem of finding a common solution to split generalized mixed equilibrium problem and fixed point problem for quasi-$% \phi $-nonexpansive mappings in 2-uniformly convex and uniformly smooth Banach space $E_1$ and a smooth, strictly convex, and reflexive Banach space $% E_2$. An iterative algorithm with Armijo linesearch rule for solving the problem is presented and its strong convergence theorem is established. The convergence result is obtained without using the hybrid method which is mostly used when strong convergence is desired. Finally, numerical experiments are presented to demonstrate the practicability, efficiency, and performance of our algorithm in comparison with other existing algorithms in the literature. Our results extend and improve many recent results in this direction.

Keywords

Split generalized mixed equilibrium problem, monotone mapping, strong convergence, Banach space, quasi-phi-nonexpansive mapping, linesearch rule

First Page

1146

Last Page

1170

Recommended Citation

Oyewole, Olawale; MEWOMO, OLUWATOSIN; JOLAOSO, LATEEF; and KHAN, Safeer Hussain (2020) "An extragradient algorithm for split generalized equilibrium problem and the set of fixed points ofquasi-$\phi $-nonexpansive mappings in Banach spaces," Turkish Journal of Mathematics: Vol. 44: No. 4, Article 6. https://doi.org/10.3906/mat-1911-83
Available at: https://journals.tubitak.gov.tr/math/vol44/iss4/6