This paper gives a study of various types of cone metric spaces and its topological characterizations, and considers some generalized contraction type of mappings on θ-complete cone metric like spaces, then generalizes some previous coupled fixed point theorems in this setting.

in this manuscript,we depict the concept of composed operators and then establish the existence and uniqueness of coupled coincidence points of such contractions and other related mappings in the abstract framework of multiplicative cone metric space over Banach algebra with multiplicative algebra solid cone regardless of its normality property. Further, we give illustrative examples to demonstrate the validity of our results proved herein, Eventually, we introduce an application of non-linear integral equations for the existence of a unique solution to support our results. In doing so, we show that some prvious results are consequences of our main presentd results.

Abstract. In this paper, let (X;C;DC; 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 spectral radius greater than or equal one and T from X xX to X be a generalized contraction mapping its parametric contractions are vectors in C, with these settings and without relying on the assumptions of normality and solidness of C we proved the existence of coupled coincidence points of the mapping T and hence generalized many theorems concerned with the existence of coupled coincidence points of such types and we supported these results with some illustrative examples.