Fixed Point Results of Miculescu‐Mihail, Mitrović‐Hussain, and Boyd‐Wong Type in Regular Semimetric Spaces

We establish three types of nonlinear fixed point theorems in regular semimetric spaces. First, we generalize Miculescu and Mihail’s result, thereby unifying the Matkowski fixed point theorem and the Istrăţescu fixed point theorem concerning convex contractions within the semimetric framework. Second, by introducing a sufficient condition for Cauchy sequences, we prove a fixed point theorem for weak quasicontractions with comparison functions. Third, applying two foundational lemmas, we extend the Boyd‐Wong fixed point theorem to regular semimetric spaces. Our results derive the relevant theorems in metric, b ‐metric, and ultrametric spaces as special cases, which further demonstrates the generalizability of our results.