Convergence and stability of perturbed three-step iterative algorithm for completely generalized nonlinear quasivariational inequalities

摘要

In this paper, we introduce a new class of completely generalized nonlinear quasivariational inequalities and obtain its equivalence with a class of fixed point problems by using the resolvent operator technique. Using this equivalence, we develop perturbed three-step iterative algorithm for this class of completely generalized quasivariational inequalities. We establish a few existence theorems of unique solution for the class of completely generalized quasivariational inequalities involving relaxed monotone, generalized pseudocontractive and strongly monotone mappings and prove some convergence and stability results of iterative sequence generated by perturbed three-step iterative algorithm.