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

Authors: Olawale Oyewole, OLUWATOSIN MEWOMO, LATEEF JOLAOSO, Safeer Hussain KHAN

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

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