Common and Tripled Fixed Point Theorems for Hybrid Contractions in Perturbed Rectangular 𝑏-Metric Spaces

In this paper, we establish novel common fixed point and tripled coincidence point theorems by synthesizing recent advances in perturbed metric fixed point theory, potential-driven contractions, and dual rectangular b-metric spaces. First, we establish a common fixed point theorem for an alternating pair of mappings satisfying a generalized potential-difference contraction condition in complete perturbed metric spaces, thereby unifying the results of Singh and Devi with the discontinuous fixed point framework of Pant et al. Second, we establish common tripled fixed point and tripled coincidence point theorems for nonlinear mappings acting on spaces endowed with two perturbed rectangular b-metrics, generalising the theorems of Gu and Liu under perturbed error structures. Step-by-step detailed proofs are provided, accompanied by three illustrative examples verifying the conditions and highlighting the role of potential and perturbation functions. Finally, a comprehensive conclusion and full declarations are presented.