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

45 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

Access to Document

10.1515/apam-2017-0037

Cite this

@article{b5b6acf3dde04267a2510b339aefe15c,

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

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.",

keywords = "Bregman distance, Bregman projection, Fr{\'e}chet differentiable functions, G{\^a}teaux differentiable function, Legendre functions, convex minimization problem, reffexive Banach space, resolvent, strong convergence, variational inequality",

author = "Jolaoso, \{Lateef Olakunle\} and Ogbuisi, \{Ferdinard Udochukwu\} and Mewomo, \{Oluwatosin Temitope\}",

note = "Publisher Copyright: {\textcopyright} 2018 Walter de Gruyter GmbH, Berlin/Boston.",

year = "2018",

month = jul,

day = "1",

doi = "10.1515/apam-2017-0037",

language = "English",

volume = "9",

pages = "167--184",

journal = "Advances in Pure and Applied Mathematics",

issn = "1867-1152",

publisher = "ISTE Group",

number = "3",

}

TY - JOUR

T1 - An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces

AU - Jolaoso, Lateef Olakunle

AU - Ogbuisi, Ferdinard Udochukwu

AU - Mewomo, Oluwatosin Temitope

PY - 2018/7/1

Y1 - 2018/7/1

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

UR - https://www.scopus.com/pages/publications/85040225264

U2 - 10.1515/apam-2017-0037

DO - 10.1515/apam-2017-0037

M3 - Article

AN - SCOPUS:85040225264

SN - 1867-1152

VL - 9

SP - 167

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

Access to Document

Other files and links

Fingerprint

Cite this