TY - JOUR

T1 - A Unified Algorithm for Solving Split Generalized Mixed Equilibrium Problem, and for Finding Fixed Point of Nonspreading Mapping in Hilbert Spaces

AU - Jolaoso, Lateef Olakunle

AU - Oyewole, Kazeem Olawale

AU - Okeke, Chibueze Christian

AU - Mewomo, Oluwatosin Temitope

N1 - Publisher Copyright:
© 2018 by Lateef Olakunle Jolaoso et al., published by De Gruyter.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - 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.

AB - 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.

KW - accelerated algorithm

KW - fixed point problem

KW - iterative method

KW - nonspreading mapping

KW - split mixed equilibrium

KW - viscosity approximation method

UR - http://www.scopus.com/inward/record.url?scp=85056860210&partnerID=8YFLogxK

U2 - 10.1515/dema-2018-0015

DO - 10.1515/dema-2018-0015

M3 - Article

AN - SCOPUS:85056860210

VL - 51

SP - 211

EP - 232

JO - Demonstratio Mathematica

JF - Demonstratio Mathematica

SN - 0420-1213

IS - 1

ER -