Generalized fixed point theorems for asymptotically regular mappings in b-metric spaces via contractive families

This paper introduces a unified framework for fixed point theorems involving asymptotically regular mappings in b-metric spaces through the concept of contractive families. We establish a general fixed point theorem that encompasses various existing results, including those of Kannan-type and generalized contractive conditions, as special cases. In particular, we demonstrate that the recent results of Nagac and Tas [1] emerge naturally as special cases of our main theorem through appropriate parameter choices. The main result employs coefficient functions and a general auxiliary function with strengthened continuity conditions, providing flexibility that allows the derivation of numerous particular cases. Several corollaries with complete proofs are presented to demonstrate that our results properly generalize and extend well-known theorems in the literature.