POSITIVE SOLUTIONS FOR A NONLINEAR MATRIX EQUATION USING FIXED POINT RESULTS IN EXTENDED BRANCIARI b-DISTANCE SPACES

Abstract

We consider the nonlinear matrix equation (NMEs). We discuss a sufficient condition ensuringthe existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME.
In order to do this, we define FGw-contractive conditions and derive fixed points results basedon aforesaid contractive condition for a mapping in extended Branciari b-metric distancefollowed by two suitable examples. In addition, we introduce weak well-posed property,weak limit shadowing property and generalized Ulam-Hyers stability in the underlying spaceand related results.