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

In this paper, we synthesized and extended the main results of Singh and Devi [18], Pant et al. [17], and Gu and Liu [6] into unified frameworks: 1.                We formulated an alternating common fixed point theorem for a pair of mappings satisfying a potential-difference contractive condition in perturbed metric spaces. By introducing the auxiliary function, this result relaxes traditional continuity constraints and encompasses mappings exhibiting discontinuities at the boundary. 2.                We generalized common tripled fixed point and coincidence point theorems to dual perturbed rectangular-metric spaces. Detailed Cauchy convergence criteria were developed for sequences with both odd and even step lengths under rectangular topological constraints with parameter. 3.                Three analytical examples were provided to demonstrate the efficacy, consistency, and applicability of the theoretical conclusions. Future research may investigate the application of these perturbed rectangular-metric results to non-linear matrix equations, fractional boundary value problems, and coupled systems of Fredholm integral equations with perturbed kernel data.

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