Stability analysis of Gauss-type proximal point method for metrically regular mappings

In this article, we study the stability properties of a Gauss-type proximal point algorithm for solving the inclusion y ϵ T (x), where T is a set-valued mapping acting on a Banach space X with locally closed graph that is not necessarily monotone and y is a parameter. Consider a sequence of bounded constants {λk} which are away from zero. Under this consideration, we present the semi-local and local convergence of the sequence generated by an iterative method in the sense that it is stable under small variation in perturbation parameter y whenever the set-valued mapping T is metrically regular at a given point. As a result, the uniform convergence of the Gauss-type proximal point method will be established. A numerical experiment is given which illustrates the theoretical result.