ON SOLVABILITY OF GENERALIZED NONLINEAR VARIATIONAL-LIKE INEQUALITIES

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 1, 2008, pp.163-176
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.1.163

Title & Authors

ON SOLVABILITY OF GENERALIZED NONLINEAR VARIATIONAL-LIKE INEQUALITIES

Zhang, Lili; Liu, Zeqing; Kang, Shin-Min;

Zhang, Lili; Liu, Zeqing; Kang, Shin-Min;

Abstract

In this paper, we introduce and study a new class of generalized nonlinear variational-like inequalities. By employing the auxiliary principle technique we suggest an iterative algorithm to compute approximate solutions of the generalized nonlinear variational-like inequalities. We discuss the convergence of the iterative sequences generated by the algorithm in Banach spaces and prove the existence of solutions and convergence of the algorithm for the generalized nonlinear variational-like inequalities in Hilbert spaces, respectively. Our results extend, improve and unify several known results due to Ding, Liu et al, and Zeng, and others.

Keywords

generalized nonlinear variational-like inequality;auxiliary principle technique;fixed points;algorithms;reflexive Banach space;Hilbert space;

Language

English

Cited by

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