It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see  and ). In this framework, the novelty of the present paper represents the development of some fixed 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 differential equations and coupled functional equations, respectively, that are linked to the concept of sequences of contractions.
C. D. Alecsa
Babes-Bolyai University, Mihail Kogalniceanu street no. 1, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Cluj-Napoca ,Romania
Banach algebras; (G)-convergence; (H)-convergence; differential equations; fixed points; sequeneces of contractions
Cristian-Daniel Alecsa, Sequences of contractions on cone metric spaces over Banach algebras and applications to nonlinear systems of equations and systems of differential equations, International J. Nonlin. Anal. Appl., 10 (2019) 2, pp. 227-254,
International J. Nonlin. Anal. Appl.
Semnan Univ., Iran
10.22075/ijnaa.2019.18884.2040 (not working yet)
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