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 -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 -accretive mapping due to Lan et al. The result that the sequence 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 e is proved. MSC:49J40, 47H06.
Highlights
The set-valued inclusions problem, which was introduced and discussed by Bella [ ], Huang et al [ ] and Jeong [ ], is a useful extension of the mathematics analysis
Various variational inclusions have been intensively studied in recent years
Convergence analysis for the algorithm of solving a fuzzy nonlinear set-valued inclusions problem and existence analysis of a solution for the problem are explored along with some results on the resolvent operator corresponding to an (A, η)-accretive mapping due to Lan et al [ ]
Summary
The set-valued inclusions problem, which was introduced and discussed by Bella [ ], Huang et al [ ] and Jeong [ ], is a useful extension of the mathematics analysis. In , Li [ ] studied the existence of solutions and the stability of a perturbed Ishikawa iterative algorithm for nonlinear mixed quasi-variational inclusions involving (A, η)-accretive mappings in Banach spaces by using the resolvent operator technique.
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