Three-point fixed point results in \(b\)-metric spaces

The paper was RETRACTED due to irreparable mistakes and confirmation of the editor-in-chief.

Abstract

In this paper, we explore fixed-point theorems in b-metric spaces, focusing on mappings that contract the perimeters of triangles and their generalizations. We establish new fixed-point results for such mappings under specific conditions, demonstrating their existence and uniqueness in b-metric spaces. Additionally, we introduce three-point Kannan-type generalized mappings, extending classical fixed-point theorems to a broader context. These results not only generalize existing theorems but also open new directions for further research in fixed-point theory within the b-metric framework.