Some new coupled fixed point results and applications to a system of integral equations

Ümit Çakan; Rakesh Kumar; Amar  Deep

doi:10.5269/bspm.81570

Ümit Çakan
Rakesh Kumar
Amar Deep

Abstract

This paper concerns with the solvability and asymptotic stability of solutions for a class of systems of integral equations in BC (R+) which is the space of real valued, continuous and bounded functions defined on the set of nonnegative real numbers. We firstly present a theorem about existence of coupled fixed point of an operator and then we give a corollary depending on this theorem. By using this corollary we show that a class of systems of integral equations has at least one solution which is asymptotically stable. Also we give an example showing applicability of our main result. Finally we mention an open problem worth focusing on at the future.

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