In this paper, we discuss fixed point theorems for a new χ-set contraction condition in partially ordered Banach spaces, whose positive cone \(\mathbb{K}\) 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.

中文翻译：

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Banach空间上具有单调性质的非紧致性测度的局部分数阶积分方程的存在性

在本文中，我们将讨论固定点定理新χ在部分有序Banach空间-set收缩状态，其正锥\（\ mathbb {K} \）是正常的，然后进行证明一些耦合固定点定理部分有序的Banach空间。对于部分有序的Banach空间，我们放宽了基础运算符的适当域的条件。此外，我们讨论了局部分数积分方程存在的一个应用。