An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems

In this paper, we study the problem of finding a common solution of split generalized vector mixed equlibrium problem (SGVMEP), fixed point problem (FPP) and variational inequality problem (VIP). We propose an inertial-type iterative algorithm, which uses a projection onto a feasible set and a lines...

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Autores principales:	Mewomo Oluwatosin T., Oyewole Olawale K.
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	split feasibility problem vector equilibrium problem generalized mixed equilibrium problem quasi-monotone mapping strong convergence banach space 47h06 47h09 46n10 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/920e7d477fcd474aadcb240a7c1915d4
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id	oai:doaj.org-article:920e7d477fcd474aadcb240a7c1915d4
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spelling	oai:doaj.org-article:920e7d477fcd474aadcb240a7c1915d42021-12-05T14:10:45ZAn iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems2391-466110.1515/dema-2021-0019https://doaj.org/article/920e7d477fcd474aadcb240a7c1915d42021-11-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0019https://doaj.org/toc/2391-4661In this paper, we study the problem of finding a common solution of split generalized vector mixed equlibrium problem (SGVMEP), fixed point problem (FPP) and variational inequality problem (VIP). We propose an inertial-type iterative algorithm, which uses a projection onto a feasible set and a linesearch, which can be easily calculated. We prove a strong convergence of the sequence generated by the proposed algorithm to a common solution of SGVMEP, fixed point of a quasi-ϕ\phi -nonexpansive mapping and VIP for a general class of monotone mapping in 2-uniformly convex and uniformly smooth Banach space E1{E}_{1} and a smooth, strictly convex and reflexive Banach space E2{E}_{2}. Some numerical examples are presented to illustrate the performance of our method. Our result improves some existing results in the literature.Mewomo Oluwatosin T.Oyewole Olawale K.De Gruyterarticlesplit feasibility problemvector equilibrium problemgeneralized mixed equilibrium problemquasi-monotone mappingstrong convergencebanach space47h0647h0946n10MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 335-358 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	split feasibility problem vector equilibrium problem generalized mixed equilibrium problem quasi-monotone mapping strong convergence banach space 47h06 47h09 46n10 Mathematics QA1-939
spellingShingle	split feasibility problem vector equilibrium problem generalized mixed equilibrium problem quasi-monotone mapping strong convergence banach space 47h06 47h09 46n10 Mathematics QA1-939 Mewomo Oluwatosin T. Oyewole Olawale K. An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems
description	In this paper, we study the problem of finding a common solution of split generalized vector mixed equlibrium problem (SGVMEP), fixed point problem (FPP) and variational inequality problem (VIP). We propose an inertial-type iterative algorithm, which uses a projection onto a feasible set and a linesearch, which can be easily calculated. We prove a strong convergence of the sequence generated by the proposed algorithm to a common solution of SGVMEP, fixed point of a quasi-ϕ\phi -nonexpansive mapping and VIP for a general class of monotone mapping in 2-uniformly convex and uniformly smooth Banach space E1{E}_{1} and a smooth, strictly convex and reflexive Banach space E2{E}_{2}. Some numerical examples are presented to illustrate the performance of our method. Our result improves some existing results in the literature.
format	article
author	Mewomo Oluwatosin T. Oyewole Olawale K.
author_facet	Mewomo Oluwatosin T. Oyewole Olawale K.
author_sort	Mewomo Oluwatosin T.
title	An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems
title_short	An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems
title_full	An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems
title_fullStr	An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems
title_full_unstemmed	An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems
title_sort	iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/920e7d477fcd474aadcb240a7c1915d4
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An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems

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