The metric function generalizes the concept of distance between two points and hence includes the symmetric property. The aim of this article is to introduce a new and proper extension of Kannan’s fixed point theorem to the case of multivalued maps using Wardowski’s F-contraction. We show that our result is applicable to a class of mappings where neither the multivalued version of Kannan’s theorem nor that of Wardowski’s can be applied to determine the existence of fixed points. Application of our result to the solution of integral equations has been provided. A multivalued Reich type generalized version of the result is also established.

中文翻译：

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使用 Wardowski 技术对多值映射的 Kannan 和 Reich 不动点定理的新扩展以及对积分方程的应用

度量函数概括了两点之间的距离的概念，因此包括对称特性。本文的目的是将 Kannan 不动点定理引入到使用 Wardowski 的 F 收缩的多值映射情况的新的适当扩展。我们表明我们的结果适用于一类映射，其中 Kannan 定理的多值版本和 Wardowski 的多值版本都不能用于确定不动点的存在。已经提供了我们的结果在积分方程解中的应用。还建立了结果的多值 Reich 类型广义版本。