Sensitivity analysis for generalized set-valued parametric ordered variational inclusion with ( α , λ ) - N O D S M mappings in ordered Banach spaces

Hong Gang Li,Mao Ming Jin,Li Pei Li,Ji Ming Zheng

doi:10.1186/1687-1812-2014-122

Abstract

In this paper, a new class of general set-valued parametric ordered variational inclusions, , with mappings is studied in ordered Banach spaces. Then, by using fixed point theory and the resolvent operator associated with set-valued mappings, an existence theorem and a sensitivity analysis of the solution set for this kind of parametric variational inclusion is proved and discussed in ordered Banach spaces. The obtained results seem to be general in nature. MSC:49J40, 47H06.

Highlights

Generalized nonlinear ordered variational inequalities and inclusions have wide applications in many fields including, for example, mathematics, physics, optimization and control, nonlinear programming, economics, and engineering sciences etc
Nonlinear mapping fixed point theory and applications have been extensively studied in ordered Banach spaces [ – ]
In, the author introduced and studied characterizations of ordered-weak-ANODD set-valued mappings, which was applied to finding an approximate solution for a new class of general nonlinear mixed-order quasi-variational inclusions involving the ⊕ operator in ordered Banach spaces [ ], and, applying the matrix analysis and the vector-valued mapping fixed point analysis method, he introduced and studied a new class of generalized nonlinear mixed-order variational inequalities systems with ordered B-restricted-accretive mappings for ordered Lipschitz continuous mappings in ordered Banach spaces [ ]

Summary

Introduction

Generalized nonlinear ordered variational inequalities and inclusions (ordered equation) have wide applications in many fields including, for example, mathematics, physics, optimization and control, nonlinear programming, economics, and engineering sciences etc. By using the B-restricted-accretive method of the mapping A with constants α , α , the author introduced and studied a new class of general nonlinear ordered variational inequalities and equations in ordered Banach spaces [ ].

Results

Conclusion