Strong convergence theorems for variational inequality problems and quasi-φ-asymptotically nonexpansive mappings

H. Zegeye, N. Shahzad

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper, we introduce an iterative process which converges strongly to a common solution of finite family of variational inequality problems for γ-inverse strongly monotone mappings and fixed point of two continuous quasi-φ-asymptotically nonexpansive mappings in Banach spaces. Our theorems extend and unify most of the results that have been proved for the class of monotone mappings.

Original languageEnglish
Pages (from-to)101-116
Number of pages16
JournalJournal of Global Optimization
Volume54
Issue number1
DOIs
Publication statusPublished - Sep 1 2012

Fingerprint

Inverse-strongly Monotone Mapping
Asymptotically Nonexpansive Mapping
Monotone Mapping
Variational Inequality Problem
Strong Theorems
Iterative Process
Strong Convergence
Convergence Theorem
Fixed point
Banach space
Converge
Theorem
Banach spaces
Family
Class
Variational inequalities

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this

@article{cdc92960e6c1483e9853c41fb4d10e6b,
title = "Strong convergence theorems for variational inequality problems and quasi-φ-asymptotically nonexpansive mappings",
abstract = "In this paper, we introduce an iterative process which converges strongly to a common solution of finite family of variational inequality problems for γ-inverse strongly monotone mappings and fixed point of two continuous quasi-φ-asymptotically nonexpansive mappings in Banach spaces. Our theorems extend and unify most of the results that have been proved for the class of monotone mappings.",
author = "H. Zegeye and N. Shahzad",
year = "2012",
month = "9",
day = "1",
doi = "10.1007/s10898-011-9744-8",
language = "English",
volume = "54",
pages = "101--116",
journal = "Journal of Global Optimization",
issn = "0925-5001",
publisher = "Springer Netherlands",
number = "1",

}

Strong convergence theorems for variational inequality problems and quasi-φ-asymptotically nonexpansive mappings. / Zegeye, H.; Shahzad, N.

In: Journal of Global Optimization, Vol. 54, No. 1, 01.09.2012, p. 101-116.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Strong convergence theorems for variational inequality problems and quasi-φ-asymptotically nonexpansive mappings

AU - Zegeye, H.

AU - Shahzad, N.

PY - 2012/9/1

Y1 - 2012/9/1

N2 - In this paper, we introduce an iterative process which converges strongly to a common solution of finite family of variational inequality problems for γ-inverse strongly monotone mappings and fixed point of two continuous quasi-φ-asymptotically nonexpansive mappings in Banach spaces. Our theorems extend and unify most of the results that have been proved for the class of monotone mappings.

AB - In this paper, we introduce an iterative process which converges strongly to a common solution of finite family of variational inequality problems for γ-inverse strongly monotone mappings and fixed point of two continuous quasi-φ-asymptotically nonexpansive mappings in Banach spaces. Our theorems extend and unify most of the results that have been proved for the class of monotone mappings.

UR - http://www.scopus.com/inward/record.url?scp=84865145018&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865145018&partnerID=8YFLogxK

U2 - 10.1007/s10898-011-9744-8

DO - 10.1007/s10898-011-9744-8

M3 - Article

AN - SCOPUS:84865145018

VL - 54

SP - 101

EP - 116

JO - Journal of Global Optimization

JF - Journal of Global Optimization

SN - 0925-5001

IS - 1

ER -