A Unified Algorithm for Solving Split Generalized Mixed Equilibrium Problem, and for Finding Fixed Point of Nonspreading Mapping in Hilbert Spaces

Abstract

The purpose of this paper is to study a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces.We introduce a new iterative algorithm and prove its strong convergence for approximating a common solution of a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces. Our algorithm is developed by combining a modified accelerated Mann algorithm and a viscosity approximation method to obtain a new faster iterative algorithm for finding a common solution of these problems in real Hilbert spaces. Also, our algorithm does not require any prior knowledge of the bounded linear operator norm. We further give a numerical example to show the efficiency and consistency of our algorithm. Our result improves and compliments many recent results previously obtained in this direction in the literature.

Keywords

• split mixed equilibrium
• nonspreading mapping
• fixed point problem
• accelerated algorithm
• iterative method
• viscosity approximation method
• 65K15
• 47J25
• 65J15
• 90C33