Partial h−F-Generalized and Subgeneralized Chatterjea Convex Contractions in b-Metric Spaces and Some Approximate Fixed-Point Results via Admissible Mappings

In this paper, we present new approximate fixed-point and fixed-point results for partial h−F-generalized and h−F-subgeneralized Chatterjea two-sided convex contraction mappings in the setting of b-metric spaces. To establish our main results, we employ admissible mappings and integrate the concept of upclass of Type I functions with partial Chatterjea two-sided convex contraction mappings in the framework of b-metric spaces. Our approach relaxes the continuity assumptions of the mappings to comparatively less restrictive conditions, namely, α-continuity and μ-continuity. To emphasize the significance of our hypotheses in ensuring the existence of a unique fixed point, we provide appropriate examples. Specifically, our primary example illustrates that a contractive mapping can have a discontinuity at its fixed point. Additionally, applications of our main result to a b-metric space endowed with a graph and a nonlinear initial value problem involving the Caputo fractional derivatives are presented. Our main results extend and generalize several related findings in the existing literature.