Some results on coupled coincidence points in vector quasi cone metric spaces over Banach algebras with satisfactory cones

Abstract

Let (X,C,DC, ) be a complete parametric vector quasi cone metric space over a Banach algebra A, C be a cone in A that contains some semi-interior points, be a metric parameter n C with a spectral radius ( ) > 1, and T : X X ! X be a generalized contraction mapping where its parametric contractions are vectors in C, with these settings and without relying on the assumptions of normality and solidness of C, we prove the existence of coupled coincidence points of the mapping T and hence generalize many theorems concerned with the existence of coupled coincidence points of such types and we support these results with some illustrative examples.