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

Authors:
Xie Ping Ding
Affiliations:
Department of Mathematics, Sichuan Normal University, Chongdu, Sichuan 61006, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 6
Cited 11

Auxiliary problem principle extended to variational inequalities

Journal of Optimization Theory and Applications
Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications

Mathematical Programming: Series A and B
Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming

Mathematical Programming: Series A and B
General algorithm for variational inequalities

Journal of Optimization Theory and Applications
Nonconvex functions and variational inequalities

Journal of Optimization Theory and Applications
Interative schemes for solving mixed variational-like inequalites1,2

Journal of Optimization Theory and Applications

A new class of completely generalized quasi-variational inclusions in Banach spaces

Journal of Computational and Applied Mathematics
Parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings

Journal of Computational and Applied Mathematics
Existence of solutions and convergence of iterative algorithms for a system of generalized nonlinear mixed quasi-variational inclusions

Computers & Mathematics with Applications
Existence and algorithm of solutions for generalized strongly nonlinear mixed variational-like inequalities in Banach spaces

Computers & Mathematics with Applications
Iterative algorithm for finding approximate solutions of mixed quasi-variational-like inclusions

Computers & Mathematics with Applications
General iterative algorithms for solving mixed quasi-variational-like inclusions

Computers & Mathematics with Applications
Generalized mixed variational-like inequality for random fuzzy mappings

Journal of Computational and Applied Mathematics
Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces

Computers & Mathematics with Applications
The auxiliary principle and an algorithm for a system of generalized set-valued mixed variational-like inequality problems in Banach spaces

Journal of Computational and Applied Mathematics
Parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings

Journal of Computational and Applied Mathematics
Existence and algorithms for bilevel generalized mixed equilibrium problems in Banach spaces

Journal of Global Optimization

Quantified Score

Hi-index	7.30

Visualization

Abstract

In this paper, we study a new class of nonlinear mixed variational-like inequalities in reflexive Banach spaces. By applying a minimax inequality due to author, we first prove an existence uniqueness theorem of solutions for the nonlinear mixed variational-like inequalities. Next, we extend the auxiliary problem technique under reflexive Banach space setting to suggest and analyze an innovative iterative algorithm to compute the approximate solutions of the nonlinear mixed variational-like inequalities. The convergence criteria of the iterative algorithm is also given. These results improve and generalize many known results in recent literature.