An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

Abstract

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

Keywords

• Fixed point theorem
• Nonlinear integral equations (NIE)
• Tripled fixed point
• Measure of noncompactness (MNC)