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Generalizations of Darbo’s fixed point theorem for new condensing operators with application to a functional integral equation

Rehman Habib ur, Gopal Dhananjay, Kumam Poom

Demonstratio Mathematica

2019

Vol. 52, nr 1

166--182

In this paper, we provide some generalizations of the Darbo’s fixed point theorem associated with the measure of noncompactness and present some results on the existence of the coupled fixed point theorems for a special class of operators in a Banach space. To acquire this result, we define α-ψ and β-ψ con-densing operators and using them we propose new fixed point results. Our results generalize and extendsome comparable results from the literature. Additionally, as an application, we apply the obtained fixedpoint theorems to study the nonlinear functional integral equations.