Parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings

AbstractA new class of parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings is introduced. By applying resolvent operator technique of h-maximal monotone mapping and the property of fixed point set of set-valued contractive mappings, the behavior and sensitivity analysis of the solution set of the parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings are studied. The continuity and Lipschitz continuity of the solution set with respect to the parameter are proved under suitable assumptions. Our approach and results are new and improve, unify and extend previous many known results in this field

Iterative process with errors to nonlinear Ф-strongly accretive operator equations in arbitrary Banach spaces

AbstractLet X be an arbitrary Banach space and T : D(T) ⊂ X → X be a Lipschitz ф-strongly accretive operator with domain D(T) and range R(T). The Mann and Ishikawa type iterative sequences with errors which strongly converge to the unique solution of the equation Tx = f under weaker conditions are given. The related results deal with the problems that the Mann and Ishikawa iterative sequences with errors strongly converge to the unique fixed point of Lipschitz ф-hemicontractive operators