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

Abstract

Let ( X , C , D C , χ ) 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, χ be a metric parameter in C with a spectral radius σ ( χ ) (cid:62) 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.