Abstract

In this paper, we will use the notion of \(\alpha \)-admissible mappings in Banach spaces, to introduce the concept of \({{T}_{\beta }}\)-contractive mappings and establish a fixed point theorem for this type of contractions. Our theorems generalize and improve many results in the literature. Moreover, we apply the main result to prove the existence of a solution for Volterra-integral equation, under more general assumptions than previously made.

中文翻译：

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一类新收缩的非紧性测度的不动点定理

摘要

在本文中，我们将使用\(\alpha \) - Banach 空间中的可容映射的概念，引入\({{T}_{\beta }}\) -收缩映射的概念并建立不动点这种收缩的定理。我们的定理概括并改进了文献中的许多结果。此外，我们应用主要结果证明了 Volterra 积分方程解的存在性，这是在比以前所做的更一般的假设下。