A new approach to fixed point theorems in compact 2-generalized metric spaces

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).