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Demonstratio Mathematica

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Volume 51, Issue 1


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
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  • School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
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Published Online: 2018-09-14 | DOI: https://doi.org/10.1515/dema-2018-0015


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

MSC 2010: 65K15; 47J25; 65J15; 90C33


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About the article

Received: 2018-03-26

Accepted: 2018-06-15

Published Online: 2018-09-14

Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 211–232, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0015.

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© by Lateef Olakunle Jolaoso et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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