Abstract The self-mappings satisfying implicit relations were introduced in a previous study [Popa, Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bacău 7 (1997), 129–133]. In this study, we introduce self-operators satisfying an ordered implicit relation and hence obtain their fixed points in the cone metric space under some additional conditions. We obtain a homotopy result as an application.

中文翻译：

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锥度量空间中的一些结果在同伦理论中的应用

摘要 满足隐式关系的自映射在先前的研究[Popa，隐式收缩映射的不动点定理，Stud。塞克。圣瑟。垫。大学 Bacău 7 (1997), 129–133]。在这项研究中，我们引入了满足有序隐式关系的自算子，从而在一些附加条件下获得它们在锥度量空间中的不动点。我们得到一个同伦结果作为一个应用。