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

Demonstratio mathematica

article

Lateef Olakunle Jolaoso¹  Kazeem Olawale Oyewole¹  Chibueze Christian Okeke¹  Oluwatosin Temitope Mewomo¹ 

[1] School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal

关键词: split mixed equilibrium;    nonspreading mapping;    fixed point problem;    accelerated algorithm;    iterative method;    viscosity approximation method;   

DOI  :  10.1515/dema-2018-0015

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY