Sensitivity analysis for parametric generalized implicit quasi-variational-like inclusions involving P- η-accretive mappings

Abstract

In this paper, using proximal-point mapping technique of P- η-accretive mapping and the property of the fixed-point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of a parametric generalized implicit quasi-variational-like inclusion involving P- η-accretive mapping in real uniformly smooth Banach space. Further, under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to the parameter. The technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in [R.P. Agarwal, Y.-J. Cho, N.-J. Huang, Sensitivity analysis for strongly nonlinear quasi-variational inclusions, Appl. Math. Lett. 13 (2002) 19–24; S. Dafermos, Sensitivity analysis in variational inequalities, Math. Oper. Res. 13 (1988) 421–434; X.-P. Ding, Sensitivity analysis for generalized nonlinear implicit quasi-variational inclusions, Appl. Math. Lett. 17 (2) (2004) 225–235; X.-P. Ding, Parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings, J. Comput. Appl. Math. 182 (2) (2005) 252–269; X.-P. Ding, C.L. Luo, On parametric generalized quasi-variational inequalities, J. Optim. Theory Appl. 100 (1999) 195–205; Z. Liu, L. Debnath, S.M. Kang, J.S. Ume, Sensitivity analysis for parametric completely generalized nonlinear implicit quasi-variational inclusions, J. Math. Anal. Appl. 277 (1) (2003) 142–154; R.N. Mukherjee, H.L. Verma, Sensitivity analysis of generalized variational inequalities, J. Math. Anal. Appl. 167 (1992) 299–304; M.A. Noor, Sensitivity analysis framework for general quasi-variational inclusions, Comput. Math. Appl. 44 (2002) 1175–1181; M.A. Noor, Sensitivity analysis for quasivariational inclusions, J. Math. Anal. Appl. 236 (1999) 290–299; J.Y. Park, J.U. Jeong, Parametric generalized mixed variational inequalities, Appl. Math. Lett. 17 (2004) 43–48].