Fixed Point Theorems for Generalized Contraction in Semi-Metric Spaces With Triangular Functions

Abstract

This paper advances a line of research in fixed point theory initiated by M. Bessenyei and Z. P\'ales, building on their introduction of the triangle function concept in [15]. By applying this concept, the study revises several well-known fixed point theorems in metric spaces, extending their applicability to semimetric spaces with triangle functions. The paper focuses on general theorems involving weak, partial, Bianchini and Chatterjea-Bianchini contractions, deriving corollaries relevant to metric spaces, $b$-metric spaces, ultrametric spaces, and distance spaces with power triangle functions. Notably, several new and interesting findings emerge in the context of weak and partial contractions.