The aim of this paper is to introduce a new condition of expansiveness which extends the class of the known expansive-type mappings in the domain of closed and bounded subsets of a metric space. For the sum of an expansive mapping in a proposed sense defined on a closed convex and bounded subset of a Banach space and a continuous and compact operator, there are proved some fixed point theorems. There are also provided some examples which motivate our research. Moreover, an application to the existence problem of periodic solutions of nonlinear integral equations with a rational part is provided.

中文翻译：

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有界集上的扩展映射及其在有理积分方程中的应用

本文的目的是引入一个新的扩展性条件，它扩展了度量空间的封闭和有界子集域中已知的扩展类型映射的类。对于在 Banach 空间的闭凸有界子集和连续紧算子上定义的建议意义上的扩展映射的和，证明了一些不动点定理。还提供了一些激励我们研究的例子。此外，还提供了对有理部分非线性积分方程周期解存在性问题的应用。