Completely generalized multivalued nonlinear quasi-variational inclusions

We introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-varia...

Full description

Saved in:
Bibliographic Details
Main Authors: Zeqing Liu, Lokenath Debnath, Shin Min Kang, Jeong Sheok Ume
Format: Article
Language:English
Published: Wiley 2002-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171202108283
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849693018546765824
author Zeqing Liu
Lokenath Debnath
Shin Min Kang
Jeong Sheok Ume
author_facet Zeqing Liu
Lokenath Debnath
Shin Min Kang
Jeong Sheok Ume
author_sort Zeqing Liu
collection DOAJ
description We introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou-Yao, Kazmi, Noor, Noor-Al-Said, Noor-Noor, Noor-Noor-Rassias, Shim-Kang-Huang-Cho, Siddiqi-Ansari, Verma, Yao, and Zhang.
format Article
id doaj-art-95df40e5995d468d930926c8a4e3b708
institution DOAJ
issn 0161-1712
1687-0425
language English
publishDate 2002-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-95df40e5995d468d930926c8a4e3b7082025-08-20T03:20:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01301059360410.1155/S0161171202108283Completely generalized multivalued nonlinear quasi-variational inclusionsZeqing Liu0Lokenath Debnath1Shin Min Kang2Jeong Sheok Ume3Department of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, ChinaDepartment of Mathematics, University of Texas, Pan American, Edinburg, Texas 78539, USADepartment of Mathematics, Gyeongsang National University, Chinju 660-701, KoreaDepartment of Applied Mathematics, Changwon National University, Changwon 641-773, KoreaWe introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou-Yao, Kazmi, Noor, Noor-Al-Said, Noor-Noor, Noor-Noor-Rassias, Shim-Kang-Huang-Cho, Siddiqi-Ansari, Verma, Yao, and Zhang.http://dx.doi.org/10.1155/S0161171202108283
spellingShingle Zeqing Liu
Lokenath Debnath
Shin Min Kang
Jeong Sheok Ume
Completely generalized multivalued nonlinear quasi-variational inclusions
International Journal of Mathematics and Mathematical Sciences
title Completely generalized multivalued nonlinear quasi-variational inclusions
title_full Completely generalized multivalued nonlinear quasi-variational inclusions
title_fullStr Completely generalized multivalued nonlinear quasi-variational inclusions
title_full_unstemmed Completely generalized multivalued nonlinear quasi-variational inclusions
title_short Completely generalized multivalued nonlinear quasi-variational inclusions
title_sort completely generalized multivalued nonlinear quasi variational inclusions
url http://dx.doi.org/10.1155/S0161171202108283
work_keys_str_mv AT zeqingliu completelygeneralizedmultivaluednonlinearquasivariationalinclusions
AT lokenathdebnath completelygeneralizedmultivaluednonlinearquasivariationalinclusions
AT shinminkang completelygeneralizedmultivaluednonlinearquasivariationalinclusions
AT jeongsheokume completelygeneralizedmultivaluednonlinearquasivariationalinclusions