Existence and iterative approximation of solutions of some systems of variational inequalities and inclusions

Authors:
Syed Huzoorul H. Khan
Affiliations:
Department of Mathematics, Aligarh Muslim University, Aligarh, India
Venue:
AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
Year:
2010

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Abstract

In this paper, we consider a system of general variational inclusions (SGVI) in q-uniformally smooth Banach spaces. Using proximal-point mapping technique, we prove the existence and uniqueness of solution and suggest a Mann type perturbed iterative algorithm for SVLI. We also discuss the convergence criteria and stability of Mann type perturbed iterative algorithm. Further, we consider a system of parametric general variational inclusions (SPGVI) corresponding to SGVI and discuss the continuity of the solution. Finally we consider a system of generalized variational inequality problems (SGVIP) in Hilbert spaces. We prove an existence theorem for auxiliary problems of SGVIP. By exploiting this theorem, an algorithm for the SGVIP is constructed. Further, we prove the existence of a unique solution of SGVIP and discuss the convergence analysis of the algorithm. The techniques and results presented here improve the corresponding techniques and results for the variational inequalities and inclusions in the literature.