Sequences of contractions on cone metric spaces over Banach algebras and applications to nonlinear systems of equations and systems of dierential equations

It is well known that xed point problems of contractive-type mappings dened on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present paper represents the development of some xed point results regarding sequences of contractions in the setting of cone metric spaces over Banach algebras. Furthermore, some examples are given in order to strengthen our new concepts. Also, based on the powerful notion of a cone metric space over a Banach algebra, we present important applications to systems of dierential equations and coupled functional equations, respectively, that are linked to the concept of sequences of contractions.