Existence and algorithm of solutions for generalized strongly nonlinear mixed variational-like inequalities in Banach spaces

Authors:
Xie Ping Ding;Jen-Chih Yao;Lu-Chuan Zeng
Affiliations:
College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan;Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

In this paper, we introduce and study a class of generalized strongly nonlinear mixed variational-like inequalities in reflexive Banach spaces. The auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for generalized strongly nonlinear mixed variational-like inequalities. First, the existence of solutions of the auxiliary problems for the generalized strongly nonlinear mixed variational-like inequalities is shown. Second, an iterative algorithm for solving the generalized strongly nonlinear mixed variational-like inequalities is constructed by using this existence result. Finally, not only the existence of solutions of the generalized strongly nonlinear mixed variational-like inequalities is shown, but also the convergence of iterative sequences generated by the algorithm is also proven.