In this paper, we are dealing with a particular type of predator–prey model in which a predator has two choices of preys with probabilities x and \(1-x\), respectively. Our aims are to analyze the behavior of predator animals in such situation and to construct a general functional equation for it, which covers all the aspects of such type of relationship. The Banach fixed point theorem is being used to investigate the existence and uniqueness results of the proposed predator–prey model; Hyers–Ulam and Hyers–Ulam–Rassias type stability of the functional equation has also been discussed in it.

中文翻译：

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不动点法逼近概率捕食－被捕食模型的一个解

在本文中，我们正在处理一种特殊的捕食者－食饵模型，在这种模型中，捕食者有两种选择，分别具有概率x和\（1-x \）。我们的目的是分析这种情况下捕食动物的行为，并为其构建一个通用的函数方程，该方程涵盖此类关系的所有方面。Banach不动点定理被用于研究所提出的捕食者－被捕食者模型的存在性和唯一性结果。还讨论了功能方程的Hyers–Ulam和Hyers–Ulam–Rassias类型稳定性。