On Mixed Equilibrium Problems in Hadamard Spaces

On Mixed Equilibrium Problems in Hadamard Spaces

The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-con...

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Main Authors: Chinedu Izuchukwu, Kazeem Olalekan Aremu, Olawale Kazeem Oyewole, Oluwatosin Temitope Mewomo, Safeer Hussain Khan
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2019/3210649
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spelling doaj-18d9942b95154a59bf6ffdce3647600c2020-11-25T01:29:08ZengHindawi LimitedJournal of Mathematics2314-46292314-47852019-01-01201910.1155/2019/32106493210649On Mixed Equilibrium Problems in Hadamard SpacesChinedu Izuchukwu0Kazeem Olalekan Aremu1Olawale Kazeem Oyewole2Oluwatosin Temitope Mewomo3Safeer Hussain Khan4School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaDepartment of Mathematics, Statistics and Physics, Qatar University, Doha, QatarThe main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature.http://dx.doi.org/10.1155/2019/3210649
collection DOAJ
language English
format Article
sources DOAJ
author Chinedu Izuchukwu
Kazeem Olalekan Aremu
Olawale Kazeem Oyewole
Oluwatosin Temitope Mewomo
Safeer Hussain Khan
spellingShingle Chinedu Izuchukwu
Kazeem Olalekan Aremu
Olawale Kazeem Oyewole
Oluwatosin Temitope Mewomo
Safeer Hussain Khan
On Mixed Equilibrium Problems in Hadamard Spaces
Journal of Mathematics
author_facet Chinedu Izuchukwu
Kazeem Olalekan Aremu
Olawale Kazeem Oyewole
Oluwatosin Temitope Mewomo
Safeer Hussain Khan
author_sort Chinedu Izuchukwu
title On Mixed Equilibrium Problems in Hadamard Spaces
title_short On Mixed Equilibrium Problems in Hadamard Spaces
title_full On Mixed Equilibrium Problems in Hadamard Spaces
title_fullStr On Mixed Equilibrium Problems in Hadamard Spaces
title_full_unstemmed On Mixed Equilibrium Problems in Hadamard Spaces
title_sort on mixed equilibrium problems in hadamard spaces
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2019-01-01
description The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature.
url http://dx.doi.org/10.1155/2019/3210649
work_keys_str_mv AT chineduizuchukwu onmixedequilibriumproblemsinhadamardspaces
AT kazeemolalekanaremu onmixedequilibriumproblemsinhadamardspaces
AT olawalekazeemoyewole onmixedequilibriumproblemsinhadamardspaces
AT oluwatosintemitopemewomo onmixedequilibriumproblemsinhadamardspaces
AT safeerhussainkhan onmixedequilibriumproblemsinhadamardspaces
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