Research Article

Some Advances in Non-Archimedean Modular Metric Spaces with a Graph

Volume: 1 Number: 1 December 29, 2025

Some Advances in Non-Archimedean Modular Metric Spaces with a Graph

Abstract

This publication presents a framework for a new contraction mapping, thereby enhancing the basic theoretical notions in non-Archimedean modular metric spaces. Also, we define a basic $\theta-$$G-$contraction and give an application to graph theory using this new contraction.

Keywords

$\theta-$contractions, Non-Archimedean modular metric space, Graph theory

References

  1. [1] A. Benterki, Some data dependence results from using $C$-class functions in partial metric spaces, Univ. J. Math. Appl., 7(4) (2024), 152–162. https://doi.org/10.32323/ujma.1466879
  2. [2] O. Duman, Controllability analysis of fractional order delay differential equations via contraction principle, J. Math. Sci. Model., 7(3) (2024), 121–127. https://doi.org/10.33187/jmsm.1504151
  3. [3] N. Saleem, H. Ahmad, H. Aydi, Y. U. Gaba, On some coincidence best proximity point results, J. Math., 2021(1) (2021), Article ID 8005469. https://doi.org/10.1155/2021/8005469
  4. [4] N. Saleem, H. Işık, S. Khaleeq, C. Park, Interpolative Ciric–Reich–Rus-type best proximity point results with applications, AIMS Math., 7(6) (2022), 9731–9747. https://doi.org/10.3934/math.2022542
  5. [5] S. Bashir, N. Saleem, S. M. Husnine, Fixed point results of a generalized reversed $F$-contraction mapping and its application, AIMS Math., 6(8) (2021), 8728–8741. https://doi.org/10.3934/math.2021507
  6. [6] A. Latif, N. Saleem, M. Abbas, $\alpha$-optimal best proximity point result involving proximal contraction mappings in fuzzy metric space, J. Nonlinear Sci. Appl., 10 (2017), 92–103. https://doi.org/10.22436/jnsa.010.01.09
  7. [7] V. V. Chistyakov, Modular metric spaces. I: Basic concepts, Nonlinear Anal., 72(1) (2010), 1–14. https://doi.org/10.1016/j.na.2009.04.057
  8. [8] V. V. Chistyakov, Modular metric spaces. II: Application to superposition operators, Nonlinear Anal., 72 (2010), 15–30. https://doi.org/10.1016/j.na.2009.04.018
  9. [9] E. Girgin, A. Büyükkaya, N. K. Kuru, M. Younis, M. Öztürk, Analysis of Caputo-type nonlinear fractional differential equations and their Ulam–Hyers stability, Fractal Fract., 8(10) (2024), Article ID 558. https://doi.org/10.3390/fractalfract8100558
  10. [10] E. Girgin, A. Büyükkaya, N. K. Kuru, M. Öztürk, On the impact of some fixed point theorems on dynamic programming and RLC circuit models in $R$-modular $b$-metric-like spaces, Axioms, 13(7) (2024), Article ID 441. https://doi.org/10.3390/axioms13070441
APA
Girgin, E. (2025). Some Advances in Non-Archimedean Modular Metric Spaces with a Graph. Sakarya Journal of Mathematics, 1(1), 16-21. https://izlik.org/JA25EF98FY
AMA
1.Girgin E. Some Advances in Non-Archimedean Modular Metric Spaces with a Graph. Sakarya Journal of Mathematics. 2025;1(1):16-21. https://izlik.org/JA25EF98FY
Chicago
Girgin, Ekber. 2025. “Some Advances in Non-Archimedean Modular Metric Spaces With a Graph”. Sakarya Journal of Mathematics 1 (1): 16-21. https://izlik.org/JA25EF98FY.
EndNote
Girgin E (December 1, 2025) Some Advances in Non-Archimedean Modular Metric Spaces with a Graph. Sakarya Journal of Mathematics 1 1 16–21.
IEEE
[1]E. Girgin, “Some Advances in Non-Archimedean Modular Metric Spaces with a Graph”, Sakarya Journal of Mathematics, vol. 1, no. 1, pp. 16–21, Dec. 2025, [Online]. Available: https://izlik.org/JA25EF98FY
ISNAD
Girgin, Ekber. “Some Advances in Non-Archimedean Modular Metric Spaces With a Graph”. Sakarya Journal of Mathematics 1/1 (December 1, 2025): 16-21. https://izlik.org/JA25EF98FY.
JAMA
1.Girgin E. Some Advances in Non-Archimedean Modular Metric Spaces with a Graph. Sakarya Journal of Mathematics. 2025;1:16–21.
MLA
Girgin, Ekber. “Some Advances in Non-Archimedean Modular Metric Spaces With a Graph”. Sakarya Journal of Mathematics, vol. 1, no. 1, Dec. 2025, pp. 16-21, https://izlik.org/JA25EF98FY.
Vancouver
1.Ekber Girgin. Some Advances in Non-Archimedean Modular Metric Spaces with a Graph. Sakarya Journal of Mathematics [Internet]. 2025 Dec. 1;1(1):16-21. Available from: https://izlik.org/JA25EF98FY