In this paper, we present a new approach to solve fixed point theorems in compact 2-generalized metric spaces. The approach is to show that the restriction of a given 2-generalized metric to the closure of a certain orbit is a metric. By using the new approach and constructing a counterexample, we completely answer the open question about the role of the continuity of the 2-generalized metric posed in Kadelburg and Radenovic (TWMS J Pure Appl Math 5:3–13, 2014).

中文翻译：

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紧致2-广义度量空间中不动点定理的一种新方法

在本文中，我们提出了一种在紧致 2-广义度量空间中求解不动点定理的新方法。该方法是为了证明给定的 2-广义度量对某个轨道的闭合的限制是一个度量。通过使用新方法并构建反例，我们完全回答了 Kadelburg 和 Radenovic (TWMS J Pure Appl Math 5:3–13, 2014) 中提出的关于 2-广义度量的连续性的作用的开放性问题。