Stochastic approximation results for variational inequality problem using random-type iterative schemes

Real world problems are embedded with uncertainties. Therefore, to tackle these problems, one must consider probabilistic nature of the problems both in modeling and solution. In this work, concepts of convergence of the solution of variational inequality in classical functional analysis are extended to a stochastic domain for a random Mann-type iterative and Ishikawa-type iterative schemes in a Banach space. A mean square convergence result is proved for this extension.