Mann and Ishikawa Type Perturbed Iterative Algorithms for Generalized Quasivariational Inclusions

Research Article Perturbed Iterative Algorithms for Generalized Nonlinear Set-Valued Quasivariational Inclusions Involving Generalized m-Accretive Mappings

A new class of generalized nonlinear set-valued quasivariational inclusions involving generalizedm-accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized m-accretive mappings, we established the equivalence between the generalized nonlinear set-va...

Perturbed three-step approximation process with errors for a generalized implicit nonlinear quasivariational inclusions

Variational inequality theory has become a rich source of inspiration in the pure and applied mathematics. Variational inequalities not only have stimulated new results dealing with nonlinear partial differential equations, but also have been used in a large variety of problems arising in mechanics, physics, optimization and control nonlinear programming, economics and transportation equilibriu...

Generalized Nonlinear Implicit Quasivariational Inclusions

We introduce and study a new class of generalized nonlinear implicit quasivariational inclusions involving relaxed Lipschitzian mappings. We prove the existence of solution for the generalized nonlinear implicit quasivariational inclusions and construct some new stable perturbed iterative algorithms with errors. We also give an application to a class of generalized nonlinear implicit variationa...

Ishikawa type iterative algorithm for completely generalized nonlinear quasi-variational-like inclusions in Banach spaces

In this paper, we consider completely generalized nonlinear quasi-variational-like inclusions in Banach spaces and propose an Ishikawa type iterative algorithm for computing their approximate solutions by applying the new notion of Jη-proximal mapping given in [R. Ahmad, A.H. Siddiqi, Z. Khan, Proximal point algorithm for generalized multi-valued nonlinear quasi-variational-like inclusions in B...

On the Convergence for an Iterative Method for Quasivariational Inclusions