Iterative approximation of common solution of variational inequality and certain optimization problems with multiple output sets in Hadamard space-Reference-Cited by-同舟云学术

Iterative approximation of common solution of variational inequality and certain optimization problems with multiple output sets in Hadamard space

Published:2024-01-03 Issue:0 Volume:0 Page:
ISSN:0174-4747
Container-title:Analysis
language:en
Short-container-title:

Author:

Abass Hammed Anuoluwapo¹^ORCID,Oyewole Olawale Kazeem²^ORCID,Onifade Olayinka Martins³,Narain Ojen Kumar³

Affiliation:

1. Department of Mathematics and Applied Mathematics , Sefako Makgatho Health Sciences University , P. O. Box 94 , Pretoria 0204 , South Africa

2. Department of Mathematics , The Technion-Israel Institute of Technology , Haifa , Israel

3. School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban , South Africa

Abstract

Abstract In this paper, our main interest is to propose a viscosity iterative method for approximating solutions of variational inequality problems, resolvents of monotone operators and fixed points of ρ-demimetric mappings with multiple output sets in Hadamard spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. Also, we present an application of our main result to a convex minimization problem. Our results improve and generalize many related results in the literature.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Numerical Analysis,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anly-2022-1075/pdf

Reference37 articles.

1. H. A. Abass, K. O. Aremu, L. O. Jolaoso and O. T. Mewomo, An inertial forward-backward splitting method for approximating solutions of certain optimization problem, J. Nonlinear Funct. Anal. 2020 (2020), Article ID 6.

2. H. A. Abass, C. Izuchukwu and K. O. Aremu, A common solution of family of minimization problem and fixed point problem for multivalued type-one demicontractive-type mappings, Adv. Nonlinear Var. Inequal. 21 (2018), no. 2, 94–108.

3. H. A. Abass, A. A. Mebawondu, K. O. Aremu and O. K. Oyewole, Generalized viscosity approximation method for minimization and fixed point problems of quasi-pseudocontractive mappings in Hadamard spaces, Asian-Eur. J. Math. 15 (2022), no. 11, Paper No. 2250188.

4. B. Ahmadi Kakavandi and M. Amini, Duality and subdifferential for convex functions on complete CAT ⁢ ( 0 ) {\rm CAT}(0) metric spaces, Nonlinear Anal. 73 (2010), no. 10, 3450–3455.

5. S. Alizadeh, H. Dehghan and F. Moradlou, Δ-convergence theorems for inverse-strongly monotone mappings in CAT ⁢ ( 0 ) \rm{CAT}(0) spaces, Fixed Point Theory 19 (2018), no. 1, 45–56.