Stochastic Approximation Result for Random Split Variational Inequality Problems in Hilbert Spaces

Abstract

This study aims at extending the idea of common solutions to problems in classical functional analysis to accommodate situations where there are randomness in the system, as real life problems are, mostly, of this nature. A common solution to random split feasibility and random variational inequality problems, called random split variational inequality problem, is sought through fixed point theory, using a nonexpansive operator.  A random type of the two-step Wang’s algorithm is used to obtain a unique solution to the problem; and a strong convergence to this unique solution is proven. The result is applied to optimal tax policy problem and is seen to be adequate in solving the problem, yielding tax rates of 14.79% and 13.91% for the two categories of businesses. This result extends, and unifies some established results in the literature on deterministic functional analysis.