In 1980, Hegedüs and Szilágyi proved some fixed point theorem in complete metric spaces. Introducing a new contractive condition, we generalize Hegedüs-Szilágyi’s fixed point theorem. We discuss the relationship between the new contractive condition and other contractive conditions. We also show that we cannot extend Hegedüs-Szilágyi’s fixed point theorem to Meir-Keeler type.

中文翻译：

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完整度量空间中Hegedüs-Szilágyi不动点定理的推广

1980年，Hegedüs和Szilágyi证明了完整度量空间中的一些不动点定理。引入新的收缩条件，我们推广了Hegedüs-Szilágyi的不动点定理。我们讨论了新的收缩条件和其他收缩条件之间的关系。我们还表明，我们无法将Hegedüs-Szilágyi的不动点定理扩展到Meir-Keeler类型。