Fixed Point Theory in Neutrosophic MR-Metric Spaces: A Unified Framework with Graph Contractions and Applications
DOI:
https://doi.org/10.19139/soic-2310-5070-3569Keywords:
Neutrosophic MR-metric spaces, fixed point theory, graph contractions, t-norm, t-conorm, Dijkstra, fuzzy logic, uncertainty modelingAbstract
This paper presents a comprehensive study of fixed point theory within the framework of Neutrosophic MR-Metric Spaces (NMR-MS), which generalize classical metric spaces by incorporating neutrosophic logic to handle uncertainty, indeterminacy, and truth degrees. We introduce a novel fixed point theorem for graph contractions in complete NMR-MS, ensuring the existence and uniqueness of fixed points under mild conditions. Additionally, we establish a graph-theoretic representation of NMR-MS and propose a modified Dijkstra’s algorithm for optimal pathfinding under neutrosophic constraints. The theoretical developments are supported by illustrative examples and applications in wireless networks, sensor systems, and fractional calculus. Our results extend and unify several existing fixed point theorems in various generalized metric spaces, including \( b \)-metric, \( M^* \)-metric, and \( \Omega \)-distance spaces.Downloads
Published
2026-08-01
How to Cite
Malkawi, A. A.-R., & Rabaiah, A. (2026). Fixed Point Theory in Neutrosophic MR-Metric Spaces: A Unified Framework with Graph Contractions and Applications. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-3569
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Research Articles
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Copyright (c) 2026 Abed Al-Rahman Malkawi, Ayat Rabaiah
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