Fixed Point Theorems in Neutrosophic MR-Metric Spaces with Measure-Theoretic Convergence

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-24-2026-61
Published: Mar 12, 2026
Cite as:
Abed Al-Rahman M. Malkawi, Ayat M. Rabaiah, Fixed Point Theorems in Neutrosophic MR-Metric Spaces with Measure-Theoretic Convergence, Int. J. Anal. Appl., 24 (2026), 61.

Main Article Content

Abed Al-Rahman M. Malkawi, Ayat M. Rabaiah

Abstract

In this paper, we introduce and study the concept of Neutrosophic MR-Metric Spaces (NMR-MS), which combine the structure of MR-metric spaces with neutrosophic membership functions. We establish a fixed point theorem for neutrosophic contraction mappings in such spaces and prove the existence, uniqueness, and measure-theoretic convergence of the fixed point. Our results extend classical fixed point theory to a more general framework that incorporates uncertainty and vagueness, as modeled by neutrosophic logic. The convergence is shown to be exponential in measure and stable under the induced measure structure. Several illustrative examples and applications are provided to validate the theoretical findings and demonstrate their applicability in dynamical systems, optimization, and stability analysis under uncertainty.

Article Details

References

  1. A. Malkawi, A. Talafhah, W. Shatanawi, Coincidence and Fixed Point Results for $(psi, L)$-M-Weak Contraction Mapping on Mb-Metric Spaces, Italian J. Pure Appl. Math. 47 (2022), 751–768.
  2. A.A.M. Malkawi, A. Rabaiah, W. Shatanawi, A. Talafhah, MR–Metric Spaces with Applications, J. Interdiscip. Math. 28 (2025), 2837–2865. https://doi.org/10.47974/jim-2275.
  3. T. Qawasmeh, $(H,Omega_b)$-Interpolative Contractions in $Omega_b$-Distance Mappings with Application, Eur. J. Pure Appl. Math. 16 (2023), 1717–1730. https://doi.org/10.29020/nybg.ejpam.v16i3.4819.
  4. A. Malkawi, A. Talafhah, W. Shatanawi, Coincidence and Fixed Point Results for Generalized Weak Contraction Mapping on b-Metric Spaces, Nonlinear Funct. Anal. Appl. 26 (2021), 177–195. https://doi.org/10.22771/nfaa.2021.26.01.13.
  5. R. Al-deiakeh, M. Alquran, M. Ali, S. Qureshi, S. Momani, et al., Lie Symmetry, Convergence Analysis, Explicit Solutions, and Conservation Laws for the Time-Fractional Modified Benjamin-Bona-Mahony Equation, J. Appl. Math. Comput. Mech. 23 (2024), 19–31. https://doi.org/10.17512/jamcm.2024.1.02.
  6. T. Qawasmeh, $H$-Simulation Functions and $Omega_b$-Distance Mappings in the Setting of $G_b$-Metric Spaces and Application, Nonlinear Funct. Anal. Appl. 28 (2023), 557–570. https://doi.org/10.22771/nfaa.2023.28.02.14.
  7. W. Shatanawi, G. Maniu, A. Bataihah, F.B. Ahmad, Common Fixed Points for Mappings of Cyclic Form Satisfying Linear Contractive Conditions With Omega-Distance, UPB Sci. Bull. Ser. A: Appl. Math. Phys. 79 (2017), 11–20.
  8. A. Bataihah, T. Qawasmeh, I. Batiha, I. Jebril, T. Abdeljawad, Gamma Distance Mappings With Application to Fractional Boundary Differential Equation, J. Math. Anal. 15 (2024), 99–106. https://doi.org/10.54379/jma-2024-5-7.
  9. K. Abodayeh, T. Qawasmeh, W. Shatanawi, A. Tallafha, $epsilon_{varphi}$-Contraction and Some Fixed Point Results via Modified $omega$-Distance Mappings in the Frame of Complete Quasi Metric Spaces and Applications, Int. J. Electr. Comput. Eng. 10 (2020), 3839–3853. https://doi.org/10.11591/ijece.v10i4.pp3839-3853.
  10. T. Qawasmeh, A. Tallafha, W. Shatanawi, Fixed and Common Fixed Point Theorems Through Modified $omega$-Distance Mappings, Nonlinear Funct. Anal. Appl. 24 (2019), 221–239.
  11. A. Bataihah, T. Qawasmeh, M. Shatnawi, Discussion on b-Metric Spaces and Related Results in Metric and G-Metric Spaces, Nonlinear Funct. Anal. Appl. 27 (2022), 233–247.
  12. T. Qawasmeh, W. Shatanawi, A. Bataihah, A. Tallafha, Common Fixed Point Results for Rational $(alpha,beta)_phi$-m$omega$ Contractions in Complete Quasi Metric Spaces, Mathematics 7 (2019), 392. https://doi.org/10.3390/math7050392.
  13. A. Bataihah, A. Tallafha, W. Shatanawi, Fixed Point Results With $Omega$-Distance by Utilizing Simulation Functions, Italian J. Pure Appl. Math. 43 (2017), 185–196.
  14. W. Shatanawi, A. Bataihah, A. Pitea, Fixed and Common Fixed Point Results for Cyclic Mappings of $Omega$-Distance, J. Nonlinear Sci. Appl. 09 (2016), 727–735. https://doi.org/10.22436/jnsa.009.03.02.
  15. A.A. Hazaymeh, A. Bataihah, Neutrosophic Fuzzy Metric Spaces and Fixed Points for Contractions of Nonlinear Type, Neutrosophic Sets Syst. 77 (2025), 96–112.
  16. A. Rabaiah, A. Tallafha, W. Shatanawi, Common Fixed Point Results for Mappings Under Nonlinear Contraction of Cyclic Form in b-Metric Spaces, Adv. Math.: Sci. J. 26 (2021), 289–301.
  17. I. Abu-Irwaq, W. Shatanawi, A. Bataihah, I. Nuseir, Fixed Point Results for Nonlinear Contractions With Generalized $Omega$-Distance Mappings, UPB Sci. Bull. Ser. A 81 (2019), 57–64.
  18. A. Bataihah, A. Hazaymeh, Quasi Contractions and Fixed Point Theorems in the Context of Neutrosophic Fuzzy Metric Spaces, Eur. J. Pure Appl. Math. 18 (2025), 5785. https://doi.org/10.29020/nybg.ejpam.v18i1.5785.
  19. I.A. Bakhtin, The Contraction Mapping Principle in Almost Metric Spaces, Funct. Anal. 30 (1989), 26–37.
  20. S. Czerwik, Contraction Mappings in b-Metric Spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5–11.
  21. T. Qawasmeh, A. Bataihah, A.A. Hazaymeh, R. Hatamleh, R. Abdelrahim, et al., New Fixed Point Results for Gamma Interpolative Contractions Through Gamma Distance Mappings, WSEAS Trans. Math. 24 (2025), 424–430. https://doi.org/10.37394/23206.2025.24.40.
  22. A. Bataihah, T. Qawasmeh, I. Batiha, I. Jebril, T. Abdeljawad, Gamma Distance Mappings With Application to Fractional Boundary Differential Equation, J. Math. Anal. 15 (2024), 99–106. https://doi.org/10.54379/jma-2024-5-7.
  23. A. Al-Zghoul, T. Qawasmeh, R. Hatamleh, A. Alhazimeh, A New Contraction by Utilizing H-Simulation Functions and $Omega$-Distance Mappings in the Frame of Complete G-Metric Spaces, J. Appl. Math. Inform. 42 (2024), 749–759. https://doi.org/10.14317/jami.2024.749.
  24. A. Bataihah, T. Qawasmeh, A New Type of Distance Spaces and Fixed Point Results, J. Math. Anal. 15 (2024), 81–90. https://doi.org/10.54379/jma-2024-4-5.
  25. A. Bataihah, Some Fixed Point Results with Application to Fractional Differential Equation via New Type of Distance Spaces, Results Nonlinear Anal. 7 (2024), 202–208. https://doi.org/10.31838/rna/2024.07.03.015.
  26. A. Malkawi, D. Mahmoud, A.M. Rabaiah, R. Al-Deiakeh, W. Shatanawi, On Fixed Point Theorems in MR-Metric Spaces, Nonlinear Funct. Anal. Appl. 29 (2024), 1125–1136.
  27. G.M. Gharib, A. Malkawi, A.M. Rabaiah, W.A. Shatanawi, M.S. Alsauodi, A Common Fixed Point Theorem in an M*-Metric Space and an Application, Nonlinear Funct. Anal. Appl. 27 (2022), 289–308. https://doi.org/10.22771/nfaa.2022.27.02.06.
  28. A.A. Malkawi, Existence and Uniqueness of Fixed Points in $MR$-Metric Spaces and Their Applications, Eur. J. Pure Appl. Math. 18 (2025), 6077. https://doi.org/10.29020/nybg.ejpam.v18i2.6077.
  29. A.A. Malkawi, Convergence and Fixed Points of Self-Mappings in MR-Metric Spaces: Theory and Applications, Eur. J. Pure Appl. Math. 18 (2025), 5952. https://doi.org/10.29020/nybg.ejpam.v18i2.5952.
  30. A.A.M. Malkawi, Fixed Point Theorem in MR-Metric Spaces VIA Integral Type Contraction, WSEAS Trans. Math. 24 (2025), 295–299. https://doi.org/10.37394/23206.2025.24.28.
  31. T. Qawasmeh, A.A. Malkawi, Fixed Point Theory in MR-Metric Spaces Fundamental Theorems and Applications to Integral Equations and Neutron Transport, Eur. J. Pure Appl. Math. 18 (2025), 6440. https://doi.org/10.29020/nybg.ejpam.v18i3.6440.
  32. A.A. Malkawi, Enhanced Uncertainty Modeling Through Neutrosophic MR-Metrics: A Unified Framework with Fuzzy Embedding and Contraction Principles, Eur. J. Pure Appl. Math. 18 (2025), 6475. https://doi.org/10.29020/nybg.ejpam.v18i3.6475.
  33. A.A. Malkawi, A. Rabaiah, MR-Metric Spaces: Theory and Applications in Weighted Graphs, Expander Graphs, and Fixed-Point Theorems, Eur. J. Pure Appl. Math. 18 (2025), 6525. https://doi.org/10.29020/nybg.ejpam.v18i3.6525.
  34. A.A. Malkawi, A. Rabaiah, Applications of MR-Metric Spaces in Measure Theory and Convergence Analysis, Eur. J. Pure Appl. Math. 18 (2025), 6528. https://doi.org/10.29020/nybg.ejpam.v18i3.6528.
  35. A.A. Malkawi, Compactness and Separability in MR-Metric Spaces with Applications to Deep Learning, Eur. J. Pure Appl. Math. 18 (2025), 6592. https://doi.org/10.29020/nybg.ejpam.v18i3.6592.
  36. G.M. Gharib, M.S. Alsauodi, A. Guiatni, M.A. Al-Omari, A.A.M. Malkawi, Using Atomic Solution Method to Solve the Fractional Equations, in: Springer Proceedings in Mathematics & Statistics, Springer, Singapore, 2023, pp. 123–129. https://doi.org/10.1007/978-981-99-0447-1_10.
  37. A. Al-Rahman M. Malkawi, A.M. Rabaiah, MR-Metric Spaces: Theory and Applications in Fractional Calculus and Fixed-Point Theorems, Neutrosophic Sets Syst. 90 (2025), 1103–1121.
  38. A. Al-Rahman M. Malkawi, A.M. Rabaiah, MR-Metric Spaces: Theory and Applications in Fractional Calculus and Fixed-Point Theorems, Neutrosophic Sets Syst. 91 (2025), 685–703.
  39. A.A.R.M. Malkawi, Fixed Point Theorems for Fuzzy Mappings in Neutrosophic MR-Metric Spaces, J. Nonlinear Model. Anal. Accepted.
  40. N. Anakira, I.H. Jebril, O. Ogilat, I.M. Batiha, T. Sasa, et al., Variable Fractional-Order Reaction-Diffusion System for Edge Preservation in Biomedical Imaging, Int. J. Anal. Appl. 24 (2026), 23. https://doi.org/10.28924/2291-8639-24-2026-23.
  41. A. Almalkawi, A. Amourah, A. Alsoboh, J. Salah, K. Al Mashrafih, et al., Analytic Estimates for Bi-Univalent Functions Associated with a New Operator Involving the q–Rabotnov Function, Int. J. Anal. Appl. 24 (2026), 1. https://doi.org/10.28924/2291-8639-24-2026-1.
  42. A. Malkawi, Fixed Point Theorems for Fuzzy Mappings in Mr-Metric Spaces, Nonlinear Funct. Anal. Appl. 30 (2025), 1083–1094. https://doi.org/10.22771/nfaa.2025.30.04.06.
  43. A. Malkawi, A. Rabaiah, Fuzzy Metric Spaces: Theory and Applications in Medical Imaging, Transportation, and Social Networks, Nonlinear Funct. Anal. Appl. 30 (2025), 1255–1272. https://doi.org/10.22771/nfaa.2025.30.04.17.
  44. A.A.M. Malkawi, A.M. Rabaiah, Neutrosophic MR-Metric Spaces: A Topos-Theoretic Framework with Applications, Int. J. Anal. Appl. 23 (2025), 333. https://doi.org/10.28924/2291-8639-23-2025-333.
  45. A.H. Ganie, N.E.M. Gheith, Y. Al-Qudah, A.H. Ganie, S.K. Sharma, et al., An Innovative Fermatean Fuzzy Distance Metric with Its Application in Classification and Bidirectional Approximate Reasoning, IEEE Access 12 (2024), 4780–4791. https://doi.org/10.1109/access.2023.3348780.
  46. N. Hassan, Y. Al-Qudah, Fuzzy Parameterized Complex Multi-Fuzzy Soft Set, J. Phys.: Conf. Ser. 1212 (2019), 012016. https://doi.org/10.1088/1742-6596/1212/1/012016.
  47. Y. Al-Qudah, A. Jaradat, S.K. Sharma, V.K. Bhat, Mathematical Analysis of the Structure of One-Heptagonal Carbon Nanocone in Terms of Its Basis and Dimension, Phys. Scr. 99 (2024), 055252. https://doi.org/10.1088/1402-4896/ad3add.
  48. Y. Yousef, A.O. Hamadameen, N.A. Kh, F.A. Al-Sharqi, A New Generalization of Interval-Valued Q-Neutrosophic Soft Matrix and Its Applications, Int. J. Neutrosophic Sci. 25 (2025), 242–257. https://doi.org/10.54216/ijns.250322.
  49. Y.A. Al-Qudah, F.A. Al-Sharqi, M. Mishlish, M.M. Rasheed, Hybrid Integrated Decision-Making Algorithm Based on AO of Possibility Interval-Valued Neutrosophic Soft Settings, Int. J. Neutrosophic Sci. 22 (2023), 84–98. https://doi.org/10.54216/ijns.220306.
  50. A. Yousef, K. Alhazaymeh, N. Hassan, H. Qoqazeh, M. Almousa, et al., Transitive Closure of Vague Soft Set Relations and Its Operators, Int. J. Fuzzy Log. Intell. Syst. 22 (2022), 59–68. https://doi.org/10.5391/ijfis.2022.22.1.59.
  51. H. Qoqazeh, Y. Al-Qudah, M. Almousa, A. Jaradat, On D-Compact Topological Spaces, J. Appl. Math. Inform. 39 (2021), 883–894. https://doi.org/10.14317/JAMI.2021.883.
  52. Y.A. Al-Qudah, A Robust Framework for the Decision-Making Based on Single-Valued Neutrosophic Fuzzy Soft Expert Setting, Int. J. Neutrosophic Sci. 23 (2024), 195–210. https://doi.org/10.54216/ijns.230216.
  53. Y. Al-qudah, M. Alaroud, H. Qoqazeh, A. Jaradat, S.E. Alhazmi, et al., Approximate Analytic–Numeric Fuzzy Solutions of Fuzzy Fractional Equations Using a Residual Power Series Approach, Symmetry 14 (2022), 804. https://doi.org/10.3390/sym14040804.