Random variational-like inclusion and random proximal operator equation for random fuzzy mappings in Banach spaces

In this paper, we introduce and study a random variational-like inclusion and its corresponding random proximal operator equation for random fuzzy mappings. It is established that the random variational-like inclusion problem for random fuzzy mappings is equivalent to a random fixed point problem. We also establish a relationship between random variational-like inclusion and random proximal operator equation for random fuzzy mappings. This equivalence is used to define an iterative algorithm for solving random proximal operator equation for random fuzzy mappings. Through an example, we show that the random Wardrop equilibrium problem is a special case of the random variational-like inclusion problem for random fuzzy mappings

CONVERGENCE ANALYSIS FOR APPROXIMATING SOLUTION OF VARIATIONAL INCLUSION PROBLEM

This article aims to define a new resolvent operator for variational inclusion problems in the framework of  Banach spaces. We design a rapid algorithm using the resolvent operator to approximate the solution of the variational inclusion problem in Banach spaces. Additionally, we show that the algorithm articulated in this article converges faster than the well-known and notable algorithm due to Fang and Huang. To show the superiority and prevalence of the obtained results, we propound a numerical and computational example upholding our claim.  Lastly, a minimization problem is solved with the help of the proposed algorithm, which is the first attempt in the current context of the study