MR–Metric spaces with applications
*Abed Al-Rahman M. MalkawiCorresponding authora.malkawi@aau.edu.joDepartment of Mathematics Faculty of Arts and Sciences Amman Arab UniversityAmman, 11953, Jordan0000-0002-7621-2347View full profile → , Ayat Rabaiaha.rabaiah@aau.edu.joDepartment of Mathematics Faculty of Arts and Sciences Amman Arab UniversityAmman, 11953, Jordan0009-0002-9127-149XView full profile → , Wasfi Shatanawiwshatanawi@psu.edu.sa; swasfi@hu.edu.joDepartment of Mathematics and Sciences Prince Sultan University; Department of Mathematics Faculty of Science The Hashemite University P. O. Box 330127Department of Mathematics and Sciences Prince Sultan UniversityRiyadh, 11586, Saudi ArabiaView full profile → , Abdallah Talafhaha.tallafha@ju.edu.joDepartment of Mathematics The University of JordanAmman, 11942, JordanView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Nov 2024
- Published Online:
- 05 Dec 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2275
- Pages:
- 2837–2865
Abstract
Keywords
Subject Classifications
References
[1] B. C. Dhage, “Generalized metric spaces and topological structure II,” Pure Appl. Math. Sci., vol. 40, no. 1-2, pp. 37-412 (1994).
[2] I. A. Bakhtin, “The contraction mapping principle in almost metric spaces,” Funct. Anal., vol. 30, pp. 26-37 (1989).
[3] S. Czerwik, “Contraction mappings in b-metric spaces,” Acta Math. Inform. Univ. Ostrav., vol. 1, pp. 5-11 (1993).
[4] B. C. Dhage, “Generalized metric spaces and topological structure I,” An. Şt. Univ. Al. I. Cuza Iaşi, vol. 45, pp. 3-24 (2000).
[5] S. V. R. Naidu, K. P. R. Rao, and N. S. Rao, “On the topology of D-metric spaces and the generation of D-metric spaces from metric spaces,” Int. J. Math. Sci., vol. 51, pp. 2719-2740 (2004).
[6] A. Malkawi, A. Talafhah, and W. Shatanawi, “Coincidence and fixed point results for (ψ,L)-M-weak contraction mapping on Mb-metric spaces,” Ital. J. Pure Appl. Math., no. 47, pp. 751-768 (2022).
[7] T. Qawasmeh, “(H, Ωb)-interpolative contractions in Ωb-distance mappings with applications,” Eur. J. Pure Appl. Math., vol. 16, no. 3, pp. 1717-1730 (2023), doi: 10.29020/nybg.ejpam.v16i3.4819.
[8] A. A. R. M. Malkawi, A. Talafhah, and W. Shatanawi, “Coincidence and fixed point results for generalized weak contraction mapping on b-metric spaces,” Nonlinear Funct. Anal. Appl., vol. 26, no. 1, pp. 177-195 (2021).
[9] R. Al-deiakeh, M. Alquran, M. Ali, S. Qureshi, S. Momani, and A. A. R. M. Malkawi, “Lie symmetry, convergence analysis, explicit solutions, and conservation laws for the time-fractional modified Benjamin-Bona-Mahony equation,” J. Appl. Math. Comput. Mech., vol. 23, no. 1, pp. 19-31 (2024).
[10] T. Qawasmeh, “H-simulation functions and Ω_b-distance mappings in the setting of G_b-metric spaces and application,” Nonlinear Funct. Anal. Appl., vol. 28, no. 2, pp. 557-570 (2023), doi: 10.22771/nfaa.2023.28.02.14.
[11] A. Bataihah and T. Qawasmeh, “A new type of distance spaces and fixed point results,” J. Math. Anal., vol. 15, no. 4, pp. 81-90 (2024), doi: 10.54379/jma-2024-4-5.
[12] W. Shatanawi, T. Qawasmeh, A. Bataihah, and A. Tallafha, “New contractions and some fixed point results with application based on extended quasi b-metric spaces,” U.P.B. Sci. Bull., Ser. A, vol. 83, no. 2, pp. 1223-7027 (2021).
[13] T. Qawasmeh, W. Shatanawi, A. Bataihah, and A. Tallafha, “Fixed point results and (α,β)-triangular admissibility in the frame of complete extended b-metric spaces and application,” U.P.B. Sci. Bull., Ser. A, vol. 83, no. 1, pp. 113-124 (2021).
[14] A. Bataihah, W. Shatanawi, and A. Tallafha, “Fixed point results with simulation functions,” Nonlinear Funct. Anal. Appl., vol. 25, no. 1, pp. 13-23 (2020), doi: 10.22771/nfaa.2020.25.01.02.
[15] A. A. R. M. Malkawi, D. Mahmoud, A. M. Rabaiah, R. Al-Deiakeh, and W. Shatanawi, “On fixed point theorems in MR-metric spaces,” Nonlinear Funct. Anal. Appl., pp. 1125-1136 (2024).
[16] G. M. Gharib, A. A. R. M. Malkawi, A. M. Rabaiah, W. A. Shatanawi, and M. S. Alsauodi, “A common fixed point theorem in an M*-metric space and an application,” Nonlinear Funct. Anal. Appl., vol. 27, no. 2, pp. 289-308 (2022).
[17] K. Abodayeh, W. Shatanawi, A. Bataihah, and A. H. Ansari, “Some fixed point and common fixed point results through Ω-distance under nonlinear contractions,” Gazi Univ. J. Sci., vol. 30, no. 1, pp. 293-302 (2017).
[18] A. Bataihah, A. Tallafha, and W. Shatanawi, “Fixed point results with Ω-distance by utilizing simulation functions,” Ital. J. Pure Appl. Math., vol. 43, pp. 185-196 (2020).
[19] K. Abodayeh, A. Bataihah, and W. Shatanawi, “Generalized Ω-distance mappings and some fixed point theorems,” U.P.B. Sci. Bull., Ser. A, vol. 79, pp. 223-232 (2017).
[20] H. Aydi, M. Bota, E. Karapınar, and S. Mitrović, “A fixed point theorem for set-valued quasi-contractions in b-metric spaces,” Fixed Point Theory Appl. (2012), doi: 10.1186/1687-1812-2012-88.
[21] A. Rabaiah, A. Tallafha, and W. Shatanawi, “Common fixed point results for mappings under nonlinear contraction of cyclic form in b-metric spaces,” Adv. Math. Sci. J., vol. 26, no. 2, pp. 289-301 (2021).
[22] I. Abu-Irwaq, W. Shatanawi, A. Bataihah, and I. Nuseir, “Fixed point results for nonlinear contractions with generalized Ω-distance mappings,” U.P.B. Sci. Bull., Ser. A, vol. 81, no. 1, pp. 57-64 (2019).
[23] A. A. R. M. Malkawi, “Existence and uniqueness of fixed points in MR-metric spaces and their applications,” Eur. J. Pure Appl. Math., vol. 18, no. 2, Art. no. 6077 (2025).
[24] A. A. R. M. Malkawi, “Convergence and fixed points of self-mappings in MR-metric spaces: theory and applications,” Eur. J. Pure Appl. Math., vol. 18, no. 2, Art. no. 5952 (2025).
[25] A. A. R. M. Malkawi, “Fixed point theorem in MR-metric spaces via integral type contraction,” WSEAS Trans. Math., vol. 24, pp. 295-299 (2025).
[26] S. Al-Sharif and A. Malkawi, “Modification of conformable fractional derivative with classical properties,” Ital. J. Pure Appl. Math., vol. 44, pp. 30-39 (2020).
[27] G. M. Gharib, M. S. Alsauodi, A. Guiatni, M. A. Al-Omari, and A. A.-R. M. Malkawi, “Using atomic solution method to solve the fractional equations,” Springer Proc. Math. Stat., vol. 418, pp. 123-129 (2023).
[28] T. Qawasmeh and A. A. R. M. Malkawi, “Fixed point theory in MR-metric spaces: fundamental theorems and applications to integral equations and neutron transport,” Eur. J. Pure Appl. Math., vol. 18, no. 3, Art. no. 6440 (2025).
[29] A. A. R. M. Malkawi, “Enhanced uncertainty modeling through neutrosophic MR-metrics: a unified framework with fuzzy embedding and contraction principles,” Eur. J. Pure Appl. Math., vol. 18, no. 3, Art. no. 6475 (2025).
[30] A. A. R. M. Malkawi and A. Rabaiah, “MR-metric spaces: theory and applications in weighted graphs, expander graphs, and fixed-point theorems,” Eur. J. Pure Appl. Math., vol. 18, no. 3, Art. no. 6525 (2025).
[31] A. A. R. M. Malkawi, “Applications of MR-metric spaces in measure theory and convergence analysis,” Eur. J. Pure Appl. Math., vol. 18, no. 3, Art. no. 6528 (2025).
[32] A. A. R. M. Malkawi and A. Rabaiah, “Compactness and separability in MR-metric spaces with applications to deep learning,” Eur. J. Pure Appl. Math., vol. 18, no. 3, Art. no. 6592 (2025).
[33] A. A.-R. M. Malkawi and A. M. Rabaiah, “MR-metric spaces: Theory and applications in fractional calculus and fixed-point theorems,” Neutrosophic Sets and Systems, vol. 90, pp. 1103–1121 (2025).
[34] A. A.-R. M. Malkawi and A. M. Rabaiah, “MR-metric spaces: Theory and applications in fractional calculus and fixed-point theorems,” Neutrosophic Sets and Systems, vol. 91, pp. 685–703 (2025).
[35] A. A.-R. M. Malkawi, “Fixed Point Theorems for Fuzzy Mappings in Neutrosophic MR-Metric Spaces,” J. Nonlinear Model. Anal., to appear (2025).
[36] H. Aydi, M. Abbas, and T. Nazir, “A fixed point theorem for set-valued quasi-contractions in b-metric spaces,” Fixed Point Theory and Applications, vol. 2012, no. 88, pp. 1–13 (2012), doi: 10.1186/1687-1812-2012-88.




