Solvability and approximation for symmetric stochastic fractional differential variational inequalities system with fixed-point problem

This paper is devoted to investigating the solvability and approximation for a symmetric stochastic fractional differential variational inequalities system with fixed-point problem (SSFDVIS with FPP). Here the FPP is the fixed-point problem of a stochastic pseudocontractive mapping, and the SSFDVIS is composed of a symmetric stochastic variational inequalities system (SSVIS) and a symmetric stochastic fractional differential equations system (SSFDES). By means of a successive approximation technique and auxiliary-VIP-based resolvent operators, we prove the existence of a unique solution to the SSFDVIS with FPP under suitable conditions. Furthermore, the main results are applied to establish the existence of a unique solution for a constrained spatial price equilibria (SPE) system in a stochastic environment. Our principal contributions are as follows: (a) the standard assumptions on the cost mappings in SSVIS are relaxed; (b) the existence of a unique solution to SSFDVIS with FPP by using the successive approximation technique and auxiliary-VIP-based resolvent operators; (c) an application to the constrained SPE system in a stochastic environment is provided with weaker assumptions.