Existence of local fractional integral equation via a measure of non-compactness with monotone property on Banach spaces

Abstract

Abstract In this paper, we discuss fixed point theorems for a new χ-set contraction condition in partially ordered Banach spaces, whose positive cone K $\mathbb{K}$ is normal, and then proceed to prove some coupled fixed point theorems in partially ordered Banach spaces. We relax the conditions of a proper domain of an underlying operator for partially ordered Banach spaces. Furthermore, we discuss an application to the existence of a local fractional integral equation.

Keywords

• Measure of non-compactness
• Local fractional integral equation