Sensitivity Analysis For Parametric Completely Generalized Nonlinear Resolvent Equations And The Iteration Algorithms Of Some Nonlinear Mappings

The purpose of this paper is to investigate some subjects about nonlinear functional analysis. This paper is divided into two chapters. In Chapter I, a new class of parametric completely generalized nonlinear implicit quasivariational inequalities and a new class of parametric completely generalized nonlinear resolvent equations are introduced and studied, respectively. The equivalence between them is also established. Using the resolvent equation technique, we not only construct a new iterative algorithm but also investigate the convergence result of the iterative algorithm and the sensitivity analysis of solutions for the parametric completely generalized nonlinear resolvent equations. The results in Chapter I represent significant improvements and refinements of the recently known results in this area. In Chapter II, we engage to investigate the convergence of modified Mann iteration and modified Ishikawa iteration are equivalent to the convergence of modified multistep iteration which is introduced by Rhoades and Soltuz in Nonlinear Anal. 58(2004), 209-228, for some kinds of nonlinear mappings. Furthermore, we show that the equivalence of stability among modified Mann iteration, modified Ishikawa iteration and modified multistep iteration.2000 AMS Subject Classification: 47J20, 49J40, 47H10.Key Words: Parametric completely generalized nonlinear implicit quasivariational inequality, parametric completely generalized nonlinear resolvent equation, sensitivity analysis, modified Mann iteration, modified Ishikawa iteration, modified multistep iteration, asymptotically nonexpansive mapping in the intermediate sense, strongly successively pseudocontractive mapping.