Asymptotically regular mappings in several spaces and related fixed point theorems

In the first chapter, the fundamental definitions and concepts that will be used in the subsequent parts of the study are presented. In the second chapter, basic concepts and examples such as metric space, convergence, continuity, asymptotic regular transformation, contraction, and $b$-metric space are introduced. In the third chapter, some important extensions of fixed-point theorems are provided under the $b$-metric space structure, which is broader than the metric space structure. Here, the fixed-point theorems are examined under the concepts of asymptotic regularity and compatibility, and various applications related to asymptotic regular