Indian Journal of Industrial and Applied Mathematics
  • Year: 2016
  • Volume: 7
  • Issue: 2

Gap Functions and Error Bounds for Generalized Set-Valued Mixed Variational Inequality

1Research Scholars, Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, Uttar Pradesh, India

2Research Scholars, Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, Uttar Pradesh, India

3Professor, Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, Uttar Pradesh, India

*(Corresponding Author) E-mail-id: ahmad kalimuddin@yahoo.co.in

Abstract

In this paper, we introduce some gap functions for generalized set-valued mixed varia-tional inequalities to obtain the equivalent optimization problems for these generalized set-valued mixed variational inequalities. We use these gap functions to obtain error bounds for solutions of generalized set-valued mixed variational inequalities in Hilbert spaces. The results obtained in this paper generalize some corresponding known results in literature.

Keywords

Gap function, Error bound, Generalized set-valued mixed variational inequality, 49C25, 49J53, 90C30