An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces

Lateef Olakunle Jolaoso; Ferdinard Udochukwu Ogbuisi; Oluwatosin Temitope Mewomo

doi:10.1515/apam-2017-0037

An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces

Lateef Olakunle Jolaoso, Ferdinard Udochukwu Ogbuisi, Oluwatosin Temitope Mewomo^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

44 Citations (Scopus)

Abstract

In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.

Original language	English
Pages (from-to)	167-184
Number of pages	18
Journal	Advances in Pure and Applied Mathematics
Volume	9
Issue number	3
DOIs	https://doi.org/10.1515/apam-2017-0037
Publication status	Published - 1 Jul 2018
Externally published	Yes

Keywords

Bregman distance
Bregman projection
Fréchet differentiable functions
Gâteaux differentiable function
Legendre functions
convex minimization problem
reffexive Banach space
resolvent
strong convergence
variational inequality

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abstract = "In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.",

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AU - Jolaoso, Lateef Olakunle

AU - Ogbuisi, Ferdinard Udochukwu

AU - Mewomo, Oluwatosin Temitope

PY - 2018/7/1

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N2 - In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.

AB - In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.

KW - Bregman distance

KW - Bregman projection

KW - Fréchet differentiable functions

KW - Gâteaux differentiable function

KW - Legendre functions

KW - convex minimization problem

KW - reffexive Banach space

KW - resolvent

KW - strong convergence

KW - variational inequality

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EP - 184

JO - Advances in Pure and Applied Mathematics

JF - Advances in Pure and Applied Mathematics

IS - 3

ER -

An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces

Abstract

Keywords

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