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

Abstract

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 condensing operators and using them we propose new fixed point results. Our results generalize and extend some comparable results from the literature. Additionally, as an application, we apply the obtained fixed point theorems to study the nonlinear functional integral equations.

Keywords

• darbo fixed point theorem
• measure of noncompactness
• fixed point
• coupled fixed point
• functional integral equation
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