المجلة العالمية للعلوم التطبيقية

ABSTRACT
This paper presents a comprehensive study of fixed point theory in generalized metric spaces, focusing on three main directions: (1) the development of new fixed point results in M∗-metric and MR-metric spaces, (2) the investigation of various contraction types including (ψ,L)-weak contractions, (α, β)ϕ-mω contractions, and (H,Ωb)-interpolative contractions, and (3) applications to fractional differential equations and nonlinear analysis. We establish several fundamental theorems that extend and unify existing results in b-metric spaces, Gb-metric spaces, and Ω-distance mappings.
The work includes new findings on coincidence points, common fixed points, and fixed points for cyclic contractions, with particular attention to their applications in solving fractional equations through methods like the atomic solution method. Our results encompass both theoretical advances
in fixed point theory and practical applications to problems involving modified conformable fractional derivatives and time-fractional equations. The paper also explores connections between simulation functions, triangular admissibility, and various generalized metric space structures.

المراجع

REFERENCES
[1]   A. Malkawi, A. Talafhah, W. Shatanawi, (2022), Coincidence and fixed point Results for (ψ,L)- M- Weak Contraction Mapping on Mb-Metric Spaces, Italian journal of pure and applied mathematics, no. 47. pp 751–768.
[2]   A. Malkawi, A. Rabaiah, W. Shatanawi and A. Talafhah, (2021), MR-metric spaces and an Application, preprint.
[3]   T. Qawasmeh, (H,Ωb)- Interpolative Contractions in Ωb- Distance Mappings with Applications, European Journal of Pure and Applied Mathematics, 16(3), 1717-1730, 2023. DOI: https://doi.org/10.29020/nybg.ejpam.v16i3.4819
[4]   Malkawi, A. A. R. M., Talafhah, A., Shatanawi, W. (2021). COINCIDENCE AND FIXED POINT RESULTS FOR GENERALIZED WEAK CONTRACTION MAPPING ON b-METRIC SPACES. Nonlinear Functional Analysis and Applications, 26(1), 177-195.
[5]   Al-deiakeh, R., Alquran, M., Ali, M., Qureshi, S., Momani, S., Malkawi, A. A. R. (2024). Lie symmetry, convergence analysis, explicit solutions, and conservation laws for the timefractional modified Benjamin-Bona-Mahony equation. Journal of Applied Mathematics andComputational Mechanics, 23(1), 19-31.
[6]   T. Qawasmeh, H-Simulation functions and Ωb-distance mappings in the setting of Gb-metric spaces and application. Nonlinear Functional Analysis and Applications,28 (2), 557-570, 2023. DOI: 10.22771/nfaa.2023.28.02.14
[7]   A. Bataihah, T. Qawasmeh, A New Type of Distance Spaces and Fixed Point Results, Journal of Mathematical Analysis, 15 (4), 81-90, 2024. doi.org/10.54379/jma-2024-4-5
[8]   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., Series A, Vol. 83, No. 2, 2021, pp. 1223-7027.
[9]   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., Series A, Vol. 83, No. 1, 2021, pp. 113-124.
[10]   Bataihah, A., Shatanawi, W., and Tallafha, A. (2020). FIXED POINT RESULTS WITH SIMULATION FUNCTIONS. Nonlinear Functional Analysis and Applications, 25(1), 13-23. DOI: 10.22771/nfaa.2020.25.01.02
[11]   Malkawi, A. A. R. M., Mahmoud, D., Rabaiah, A. M., Al-Deiakeh, R., and Shatanawi, W. (2024). ON FIXED POINT THEOREMS IN MR-METRIC SPACES. Nonlinear Functional Analysis and Applications, 1125-1136.
[12]   Gharib, G. M., Malkawi, A. A. R. M., Rabaiah, A. M., Shatanawi, W. A., Alsauodi, M. S. (2022). A Common Fixed Point Theorem in an M*-Metric Space and an Application. Nonlinear Functional Analysis and Applications, 27(2), 289-308.
[13]   Abodayeh, K., Shatanawi, W., Bataihah, A., and Ansari, A. H. (2017). Some fixed point and common fixed point results through Ω-distance under nonlinear contractions. Gazi University Journal of Science, 30(1), 293-302.
[14]   Bataihah, A., Tallafha, A., and Shatanawi, W. (2020). Fixed point results with Ω-distance by utilizing simulation functions. Ital. J. Pure Appl. Math, 43, 185-196.
[15]   K. Abodayeh, A. Bataihah, and W. Shatanawi, ”Generalized Ω-Distance Mappings and Some Fixed Point Theorems,” UPB Sci. Bull. Ser. A, Vol. 79, 2017, pp. 223-232.
[16]   Qawasmeh, T., Shatanawi, W., Bataihah, A., & Tallafha, A. (2019). Common Fixed Point Results for Rational (α, β)ϕ-mω Contractions in Complete Quasi Metric Spaces. Mathematics, 7(5), 392. DOI: 10.3390/math7050392
[17]   A. Rabaiah, A. Tallafha and W. Shatanawi, Common fixed point results for mappings under nonlinear contraction of cyclic form in b-Metric Spaces, Advances in mathematics scientific journal, 2021, 26(2), pp. 289–301.
[18]   Abu-Irwaq, I., Shatanawi, W., Bataihah, A., Nuseir, I. (2019). Fixed point results for nonlinear contractions with generalized Ω-distance mappings. UPB Sci. Bull. Ser. A, 81(1), 57-64.
[19]   Malkawi, A. A. R. M. (2025). Existence and Uniqueness of Fixed Points in MR-Metric Spacesand Their Applications. EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, Vol. 18, No. 2, Article Number 6077.
[20]   Malkawi, A. A. R. M. (2025). Convergence and Fixed Points of Self-Mappings in MR-Metric Spaces: Theory and Applications. EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS,Vol. 18, No. 2, Article Number 5952.
[21]   Malkawi, A. A. R. M. (2025). Fixed Point Theorem in MR-metric Spaces VIA Integral Type Contraction. WSEAS Transactions on Mathematics, 24, 295-299.
[22]   Al-Sharif, S., and Malkawi, A. (2020). Modification of conformable fractional derivative with classical properties. Ital. J. Pure Appl. Math, 44, 30-39.
[23]   Gharib, G.M., Alsauodi, M.S., Guiatni, A., Al-Omari, M.A., Malkawi, A.A.-R.M., Using AtomicSolution Method to Solve the Fractional Equations, Springer Proceedings in Mathematics and Statistics, 2023, 418, pp. 123–129.

Article history

Received : Apr 14, 2025

Revised : Apr 19, 2025

Accepted : Jun 22, 2025

Authors Affiliations

Ethics declarations

Acknowledgment
Author Contribution
Conflicts of Interest
Funding