An Over-Relaxed (A,η,m)-Proximal Point Algorithm for System of Nonlinear Fuzzy-Set Valued Operator Equation Frameworks and Fixed Point Problems

Abstract

In order to find the common solutions for nonlinear fuzzy-set valued operator equations and fixed point problems of Lipschitz continuous operators in Hilbert spaces, the purpose of this paper is to construct a new class of over-relaxed (A,η,m)-proximal point algorithm framework with errors by using some results on the resolvent operator corresponding to (A, η, m)-maximal monotonicity. Further, the variational graph convergence analysis for this algorithm framework is investigated. Finally, some examples of applying the main result is also given. The results presented in this paper improve and generalize some well known results in recent literatures.Keywords(A, η, m)-maximal monotonicitynonlinear fuzzy-set valued operator equation and fixed point problemOver-relaxed (A, η, m)-proximal Point Algorithm with errorsvariational graphical convergence