Perturbed Ishikawa-hybrid quasi-proximal point algorithm with accretive mappings for a fuzzy system

Abstract

A new class of fuzzy general nonlinear set-valued mixed quasi-variational inclusions frameworks for a perturbed Ishikawa-hybrid quasi-proximal point algorithm using the notion of (A, η)-accretive is developed. Convergence analysis for the algorithm of solving a fuzzy nonlinear set-valued inclusions problem and existence analysis of a solution for the problem is explored along with some results on the resolvent operator corresponding to an (A, η)-accretive mapping due to Lan et al. The result that the sequence {x n } ∞ n=1 generated by the perturbed Ishikawa-hybrid quasi-proximal point algorithm converges linearly to a solution of the fuzzy general nonlinear set-valued mixed quasi-variational inclusions with the convergence rate ε is proved. MSC: 49J40; 47H06