OPSEARCH, Vol. 42, No. I, 2005 0030-3887/00$ 5.00+0.00 Operational Research Society of India Random Variational Inequality and Complementarity Problem S. Nanda and S. Pani Department of Mathematics, liT Kharagpur India-721302 Abstract In this paper we have defined Random complementarity problem and obtained some existence results for Random variational inequality and complementarity problem in reflexive Banach space and Hilbert space. Keywords Complementarity problems, variational inequalities, random variational inequalities, random complementarity problem, and random fixed points. 1. Introduction Let X be a reflexive Banach space and X* be its dual. Let K be a closed convex subset of X and T :K * 0 The value of f ex· at XEX is denoted by (f,x) 0 Then the variational inequality is defined as: Find XE K such that (Tx, y-x) 0, V ye K. The theory of variational inequality was introduced by Stampacchia in Hilbert space and then it has been studied by many researchers in various aspects. Its conception was from a practical problem due to Signorini known as Signorini problem and then its systematic theo- retical study takes place. Many researchers have generalized it in various directions and made it more applicable to real life problems. The theory of variational inequality has be- come a very powerful tool for applied mathematicians and engineers for its wide range of Paper was received in September, 2002