<abstract><p>This paper introduces a novel class of generalized $ {\alpha} $-admissible contraction types of mappings in the framework of $ {\theta} $-complete partial satisfactory cone metric spaces and proves the existence and uniqueness of coincidence points for such mappings. In this setting, the topology generated and induced by the partial satisfactory cone metric is associated with semi-interior points rather than interior points of the underlying cone. In addition, some applications of the paper's main coincidence point theorems are given. The results of this paper unify, extend and generalize some previously proved theorems in this generalized setting.</p></abstract>

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.