Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 3

New generalizations of Modular spaces

Tayebe Lal Shateri(Hakim Sabzevari University)0000-0002-5181-6558
Pages
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Publication Date
2020-06-02
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we give a characterization of $\mathcal{F}$-modulars.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, we introduce the concept of $\mathcal{F}$-modular, which is a generalization of the modular notion.
📊
Key Findings & Data:Moreover, we introduce a $K_p$-modular and $K$-modular, and then compare these concepts together.
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Conclusion & Impact:Finally, we give a characterization of $\mathcal{F}$-modulars.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Modular space · K-modular space · F-modular space

Abstract

In the present paper, we introduce the concept of $\mathcal{F}$-modular, which is a generalization of the modular notion. Moreover, we introduce a $K_p$-modular and $K$-modular, and then compare these concepts together. Finally, we give a characterization of $\mathcal{F}$-modulars.

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Cite This Article

Shateri, T. L. (2020). New generalizations of Modular spaces. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 3. https://doi.org/10.15672/hujms.531654

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References (18)

  1. A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57, 31-37, 2000.
  2. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Univ. Ostrav. 1 (1), 511, 1993.
  3. R. Fagin, R. Kumar and D. Sivakumar, Comparing top k lists, SIAM J. Discrete Math. 17 (1), 134-160, 2003.
  4. V.S. G¨ahler, 2-metrische R¨aume und ihre topologische struktur, Math. Nachr. 26, 115-118, 1963/1964.
  5. M. Jleli and B. Samet, A generalized metric space and related fixed point theorems, Fixed Point Theory Appl. 2015, 14 pages, 2015.
  6. M. Jleli and B. Samet, On a new generalization of metric spaces, Fixed Point Theory Appl. 20 (3), 20 pages, 2018.
  7. R. Kopperman and H. Pajoohesh, Generalizations of metrics and partial metrics, Hacet. J. Math. Stat. 46 (1), 9-14, 2017.
  8. S. Koshi and T. Shimogaki, On F–norms of quasi–modular spaces, J. Fac. Sci. Hokkaido Univ. Ser. I. 15 (3), 202-218, 1961.
  9. M.A. Krasnoselskii and Y.B. Rutickii, Convex functions and Orlicz spaces (in Russian), Fizmatgiz, Moskva, 1958; Translated by L.F. Boron, Noordhoff, Groningen, 1961.
  10. W.A. Luxemburg, Banach function spaces, Ph. D. Thesis, Delft University of Technology, Delft, The Netherlands, 1959.
  11. L. Maligranda, Orlicz Spaces and Interpolation, in: Seminars in Math. 5, Univ. of Campinas, Brazil, 1989.
  12. S.G. Matthews, Partial metric topology, Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. 728, 183-197, 1994.
  13. J. Musielak, Orlicz Spaces and Modular Spaces, in: Lecture Notes in Math. 1034, Springer-Verlag, Berlin, 1983.
  14. Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2), 289-297, 2006.
  15. H. Nakano, Modulared Semi-Ordered Linear Spaces, in: Tokyo Math. Book Ser. 1, Maruzen Co., Tokyo, 1950.
  16. W. Orlicz, Collected Papers, Vols. I, II, PWN, Warszawa, 1988.
  17. T.L. Shateri, C∗-algebra-valued modular spaces and fixed point theorems, J. Fixed Point Theory Appl. 19 (2), 1551-1560, 2017.
  18. S. Yamamuro, On conjugate spaces of Nakano spaces, Trans. Amer. Math. Soc. 90, 291-311, 1959.