SOME FIXED POINT RESULTS WITH T-DISTANCE SPACES IN COMPLETE B-METRIC SPACES

Authors:

Ayman Hazaymeh,

DOI NO:

https://doi.org/10.26782/jmcms.2025.03.00001

Keywords:

Banach,b-metric spaces,Fixed point,Geraghty contractions,Non-linear contraction,

Abstract

In this paper, we present an innovative type of contraction within the framework of T-distance spaces that utilize a b-metric. This advancement allows for the derivation of a new collection of fixed-point results. Additionally, we substantiate our conclusions by offering an illustrative example and showcasing a practical application. Ultimately, we have also derived several fixed-point results that are grounded in our primary findings.

Refference:

I. Abodayeh, K., Bataihah, A., and Shatanawi, W., 2017. “Generalized Ω-Distance Mappings and Some Fixed Point Theorems.” UPB Sci. Bull., Ser. A, 79, pp. 223–232.
II. 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 Univ. J. Sci., 30(1), pp. 293–302.
III. Abu-Irwaq, I., Shatanawi, W., Bataihah, A., and Nuseir, I., 2019. “Fixed Point Results for Nonlinear Contractions with Generalized Ω-Distance Mappings.” UPB Sci. Bull., Ser. A, 81(1), pp. 57–64.
IV. Al-Tawil, A., Hazaymeh, A., and Bataihah, A., 2025. “Fixed Point Results in 𝜔𝑡-Distance Mappings for Geraghty Type Contractions.” Int. J. Neutrosophic Sci., 26(1), pp. 1–14. 10.54216/IJNS.260101.
V. Aydi, H., Karapinar, E., and Postolache, M., 2012. “Tripled Coincidence Point Theorems for Weak -Contractions in Partially Ordered Metric Spaces.” Fixed Point Theory Appl., 2012, pp. 1–12.
VI. Bakhtin, I.A., 1989. “The Contraction Mapping Principle in Quasimetric Spaces.” Funct. Anal., 30, pp. 26–37.
VII. Banach, S., 1922. “Sur Les Opérations Dans Les Ensembles Abstraits Et Leur Application Aux Équations Intégrales.” Fundam. Math., 3(1), pp. 133–181.
VIII. Bataihah, A., 2024. “Some Fixed Point Results with Application to Fractional Differential Equation via New Type of Distance Spaces.” Results Nonlinear Anal., 7(3), pp. 202–208. 10.31838/rna/2024.07.03.015
IX. Bataihah, A., and Hazaymeh, A., 2025. “Neutrosophic Fuzzy Metric Spaces and Fixed Points Results with Integral Contraction Type.” Int. J. Neutrosophic Sci., 25(3), pp. 561–572. 10.54216/IJNS.250344
X. Bataihah, A., and Hazaymeh, A., 2025. “Quasi Contractions and Fixed Point Theorems in the Context of Neutrosophic Fuzzy Metric Spaces.” Eur. J. Pure Appl. Math., 18(1), p. 5785. 10.29020/nybg.ejpam.v18i1.5785.
XI. Bataihah, A., and Qawasmeh, T., 2024. “A New Type of Distance Spaces and Fixed Point Results.” J. Math. Anal., 15(4), pp. 81–90. 10.54379/jma-2024-4-5.
XII. Bataihah, A., Qawasmeh, T., Batiha, I.M., Jebril, I.H., and Abdeljawad, T., 2024. “Gama Distance Mappings with Application to Fractional Boundary Differential Equation.” J. Math. Anal., 15(5), pp. 99–106. 10.54379/jma-2024-5-7
XIII. Bataihah, A., Qawasmeh, T., and Shatnawi, M., 2022. “Discussion on b-Metric Spaces and Related Results in Metric and G-Metric Spaces.” Nonlinear Funct. Anal. Appl., 27(2), pp. 233–247. 10.22771/nfaa.2022.27.02.02
XIV. Bataihah, A., Shatanawi, W., Qawasmeh, T., and Hatamleh, R., 2020. “On H-Simulation Functions and Fixed Point Results in the Setting of ωt-Distance Mappings with Application on Matrix Equations.” Mathematics, 8(5), p. 837. 10.3390/math8050837
XV. Bataihah, A., Shatanawi, W., and Tallafha, A., 2020. “Fixed Point Results with Simulation Functions.” Nonlinear Funct. Anal. Appl., 25(1), pp. 13–23.10.2298/FIL1608343K
XVI. Bataihah, A., Tallafha, A., and Shatanawi, W., 2020. “Fixed Point Results with Ω-Distance by Utilizing Simulation Functions.” Ital. J. Pure Appl. Math., 43, pp. 185–196.
XVII. Czerwik, S., 1993. “Contraction Mappings in b-Metric Spaces.” Acta Math. Inform. Univ. Ostraviensis, 1(1), pp. 5–11.
XVIII. Geraghty, M.A., 1973. “On Contractive Mappings.” Proc. Am. Math. Soc., 40(2), pp. 604–608.
XIX. Hajjat, M., Bataihah, A., and Hazaymeh, A., 2025. “Some Results on Fixed Points in Generalized Metric Spaces via an Auxiliary Function.” Int. J. Neutrosophic Sci., 26(1), pp. 171–180. 10.54216/IJNS.260115
XX. Hazaymeh, A., and Bataihah, A., 2024. “Results on Fixed Points in Neutrosophic Metric Spaces Through the Use of Simulation Functions.” J. Math. Anal., 15(6), pp. 47–57. 10.54379/jma-2024-6-4.
XXI. Hazaymeh, A.A., and Bataihah, A., 2025. “Neutrosophic Fuzzy Metric Spaces and Fixed Points for Contractions of Nonlinear Type.” Neutrosophic Sets Syst., 77, pp. 96–112. 10.5281/zenodo.14113784
XXII. Karapınar, E., and Fulga, A., 2023. “Discussions on Proinov-C_b-Contraction Mapping on b-Metric Space.” J. Funct. Spaces, 2023(1), p. 1411808. 10.1155/2023/1411808
XXIII. Karapınar, E., Romaguera, S., and Tirado, P., 2022. “Characterizations of Quasi-Metric and G-Metric Completeness Involving w-Distances and Fixed Points.” Demonstr. Math., 55(1), pp. 939–951. 10.1515/dema-2022-0177
XXIV. Malkawi, A.R.M., Talafhah, A., and Shatanawi, W., 2021. “Coincidence and Fixed Point Results for Generalized Weak Contraction Mapping on b-Metric Spaces.” Nonlinear Funct. Anal. Appl., 26(1), pp. 177–195. 10.22771/nfaa.2021.26.01.13
XXV. Malkawi, A., Tallafha, A., and Shatanawi, W., 2022. “Coincidence and Fixed Point Results for (Ψ, L)-m-Weak Contraction Mapping on MR-Metric Spaces.” Ital. J. Pure Appl. Math., 47, pp. 751–768.
XXVI. Qawasmeh, T., Shatanawi, W., Bataihah, A., and Tallafha, A., 2019. “Common Fixed Point Results for Rational (α,β)_φ-mω Contractions in Complete Quasi Metric Spaces.” Mathematics, 7(5), p. 392. 10.3390/math7050392
XXVII. Qawasmeh, T., Shatanawi, W., Bataihah, A., and Tallafha, A., 2021. “Fixed Point Results and (α,β )-Triangular Admissibility in the Frame of Complete Extended b-Metric Spaces and Application.” UPB Sci. Bull., Ser. A Appl. Math. Phys., 1, pp. 113–124.
XXVIII. Shatanawi, W., Abodaye, K.K., and Bataihah, A., 2016. “Fixed Point Theorem Through -Distance of Suzuki Type Contraction Condition.” Gazi Univ. J. Sci., 29(1), pp. 129–133.
XXIX. Shatanawi, W., and Bataihah, A., 2021. “Remarks on G-Metric Spaces and Related Fixed Point Theorems.” Thai J. Math., 19(2), pp. 445–455. https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1168
XXX. Shatanawi, W., Maniu, G., Bataihah, A., and Ahmad, F.B., 2017. “Common Fixed Points for Mappings of Cyclic Form Satisfying Linear Contractive Conditions with Omega-Distance.” UPB Sci. Bull., Ser. A, 79, pp. 11–20.
XXXI. Shatanawi, W., Qawasmeh, T., Bataihah, A., and Tallafha, A., 2021. “New Contractions and Some Fixed Point Results with Application Based on Extended Quasi b-Metric Space.” UPB Sci. Bull., Ser. A Appl. Math. Phys., 83(2), pp. 39–48.
XXX. Hazaymeh, A. (2025). Time Fuzzy Soft Sets and its application in design-making. International Journal of Neutrosophic Science, 25(3), 37-50.
XXXI. Hazaymeh, A. (2025). Time Factor’s Impact On Fuzzy Soft Expert Sets International Journal of Neutrosophic Science,25 (3), 155-176.
XXXII. Hazaymeh, A. (2024). Time Effective Fuzzy Soft Set and Its Some Applications with and Without a Neutrosophic. International Journal of Neutrosophic Science, (2), 129-29.
XXXIII. Hazaymeh, A. A. M. (2013). Fuzzy Soft Set And Fuzzy Soft Expert Set: Some Generalizations And Hypothetical Applications (Doctoral dissertation, Universiti Sains Islam Malaysia).
XXXIV. Tahat, A. N., Ahmed, J. H., & Hazaymeh, A. (2025). Shape preserving monotonic and convex data interpolation using rational cubic ball functions. International Journal of Neutrosophic Science, 25(3), 489-89.
XXXV Al-Odat, N. A. “Modification in ratio estimator using rank set sampling.” European Journal of Scientific Research 29.2 (2009): 265-268.
XXXVI Al-Odat, N. A., et al. “Moving extreme ranked set sampling for simple linear regression.” Statistica & Applicazioni 2 (2009): 24-37.
XXXVII Odat, Naser. Epanechnikov-pareto Distribution with Application. International Journal of Neutrosophic Science, vol., no., 2025, pp. 147-155. 10.54216/IJNS.250412

View Download