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

Lateef Olakunle Jolaoso*, Kazeem Olawale Oyewole, Chibueze Christian Okeke, Oluwatosin Temitope Mewomo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)211-232
Number of pages22
JournalDemonstratio Mathematica
Volume51
Issue number1
DOIs
Publication statusPublished - 1 Sep 2018
Externally publishedYes

Keywords

  • accelerated algorithm
  • fixed point problem
  • iterative method
  • nonspreading mapping
  • split mixed equilibrium
  • viscosity approximation method

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