Solution sensitivity of generalized nonlinear parametric [InlineEquation not available: see fulltext.]-proximal operator system of equations in Hilbert spaces

Abstract

By using the new parametric resolvent operator technique associated with [InlineEquation not available: see fulltext.]-monotone operators, the purpose of this paper is to analyze and establish an existence theorem for a new class of generalized nonlinear parametric [InlineEquation not available: see fulltext.]-proximal operator system of equations with non-monotone multi-valued operators in Hilbert spaces. The results presented in this paper generalize the sensitivity analysis results of recent work on strongly monotone quasi-variational inclusions, nonlinear implicit quasi-variational inclusions, and nonlinear mixed quasi-variational inclusion systems in Hilbert spaces. MSC:49J40, 47H05, 90C33.