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It is well known that fixed point problems of contractive-type mappingsdefined on cone metric spaces over Banach algebras are not equivalent to thosein usual metric spaces (see [3] and [10]). In this framework, the novelty ofthe present paper represents the development of some fixed point resultsregarding sequences of contractions in the setting of cone metric spaces overBanach algebras. Furthermore, some examples are given in order to strengthenour new concepts. Also, based on the powerful notion of a cone metric spaceover a Banach algebra, we present important applications to systems ofdifferential equations and coupled functional equations, respectively, that arelinked to the concept of sequences of contractions.

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