International Journal For Multidisciplinary Research

E-ISSN: 2582-2160   •   Impact Factor: 9.24

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Robust Best Proximity Theorems for Interpretative Proximal Contractions with Perturbation and Roughness in Non-Triangular Metric Spaces

Author(s) Ms. Suchitra Dey, Dr. Akanksha Dubey
Country India
Abstract This paper introduces a novel framework for best proximity point theory within non- triangular metric spaces (NTMS), incorporating perturbation effects and roughness parameters. We define interpretative proximal contractions (IPCs) as a broad class of mappings that generalize existing contraction types [Anuradha & Veeramani, 2009; Karapınar & Erhan, 2011] while accommodating structural irregularities in metric spaces [Eldred & Veeramani, 2006; Basha, 2011]. Our main results establish robust existence theorems for best proximity points under IPC conditions, demonstrating stability against both systematic perturbations and random roughness in the underlying metric structure. The theoretical framework extends traditional best proximity point theory by introducing two-component metrics (D and P) that separate exact distance measurements from perturbation components, enabling more realistic modeling of irregular spaces. We provide several non-trivial examples illustrating our concepts and demonstrate applications to nonlinear boundary value problems involving thermal radiation in spacecraft structures, showing how our robust proximity theorems guarantee solution existence under metric uncertainties. By bridging the gap between idealized metric space solutions and real-world situations containing measurement errors and structural irregularities, the study advances both theoretical mathematics and applied analysis.
Keywords Perturbation analysis, robustness, roughness parameters, fixed point theory, nonlinear analysis, optimal proximity points, non-triangular metric spaces, and interpretative proximal-contractions.
Field Mathematics
Published In Volume 7, Issue 6, November-December 2025
Published On 2025-12-20
DOI https://doi.org/10.36948/ijfmr.2025.v07i06.63935
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E-ISSN 2582-2160
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