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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 18 Issue: 2

Recent Advances in the Convergence of Function Sequences in Neutrosophic Normed Spaces via Ideals

Ömer Kişi(Bartın Üniversitesi)0000-0001-6844-3092
Dr. Nesar Hossain(Dumkal Institute of Engineering and Technology)0000-0002-2205-3344
Carlos Granados(Universidad de Antioquia, Estudiante de Doctorado en Matemáticas)0000-0002-7754-1468
Pages
—
Publication Date
2026-06-30
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In addition, we derive certain foundational results concerning these concepts with respect to $(\Phi,\Psi,\Upsilon)$ in NNS.

📌 3 Key Takeaways

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Objective & Hypothesis:In this article, we introduce the notions of $\mathcal{I}$-pointwise convergence and $\mathcal{I}$-uniform convergence for sequences of functions defined on a neutrosophic normed space (NNS) with respect to the neutrosophic norm $(\Phi,\Psi,\Upsilon)$.
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Key Findings & Data:Furthermore, we establish Cauchy criteria for both $\mathcal{I}$-pointwise and $\mathcal{I}$-uniform convergence in NNS.
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Conclusion & Impact:In addition, we derive certain foundational results concerning these concepts with respect to $(\Phi,\Psi,\Upsilon)$ in NNS.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Neutrosophic normed space · $t$-norm · $t$-conorm

Abstract

In this article, we introduce the notions of $\mathcal{I}$-pointwise convergence and $\mathcal{I}$-uniform convergence for sequences of functions defined on a neutrosophic normed space (NNS) with respect to the neutrosophic norm $(\Phi,\Psi,\Upsilon)$. Furthermore, we establish Cauchy criteria for both $\mathcal{I}$-pointwise and $\mathcal{I}$-uniform convergence in NNS. In addition, we derive certain foundational results concerning these concepts with respect to $(\Phi,\Psi,\Upsilon)$ in NNS.

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Cite This Article

Kişi, Ö., Hossain, D. N., Granados, C. (2026). Recent Advances in the Convergence of Function Sequences in Neutrosophic Normed Spaces via Ideals. Turkish Journal of Mathematics and Computer Science, Volume: 18 Issue: 2. https://doi.org/10.47000/tjmcs.1815791

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References (46)

  1. Antal, R., Chawla, M., Some aspects of λ-Δm-statistical convergence on neutrosophic normed spaces, Kyungpook Math. J., 64(3)(2024), 461–478.
  2. Antal, R., Chawla, M., Kumar, V., Certain aspects of rough ideal statistical convergence on neutrosophic normed spaces, Korean J. Math., 32(1)(2024), 121–135.
  3. Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20(1986), 87–96.
  4. Bilgin, N.G., Hilbert I-statistical convergence on neutrosophic normed spaces, Gazi Univ. J. Sci. Part A: Eng. Innov., 10(1)(2023), 1–8.
  5. Bilgin, N.G., Arithmetic statistically convergent on neutrosophic normed spaces, G¨um¨us¸hane Univ. J. Sci., 13(2)(2023), 270–280.
  6. Chawla, M., Antal, R., Zweier ideal convergence sequence spaces defined by Orlicz function on neutrosophic normed spaces, TWMS J. Appl. Eng. Math., 15(5)(2025), 1063–1073.
  7. Chawla, M., Antal, R., Kaur, M., Rough λ-statistical convergence in neutrosophic normed spaces, Honam Math. J., 47(2)(2025), 141–158.
  8. Connor, J.S., The statistical and strong p–Ces`aro convergence of sequences, Analysis, 8(1988), 47–63.
  9. Fast, H., Sur la convergence statistique, Colloq. Math., 2(3-4)(1951), 241–244.
  10. Felbin, C., Finite dimensional fuzzy normed linear space, Fuzzy Sets Syst., 48(2)(1992), 239–248.
  11. Fridy, J.A., On statistical convergence, Analysis, 5(1985), 301–313.
  12. George, A., Veeramani, P., On some results in fuzzy metric spaces, Fuzzy Sets Syst., 64(1994), 395–399.
  13. Granados, C., Choudhury, C., Quasi statistical convergence in neutrosophic normed spaces for triple sequence spaces, Asian-Eur. J. Math., 16(03)(2023), 2350034.
  14. Hossain, N., Mohiuddine, S.A., On generalized difference I-convergent sequences in neutrosophic n-normed linear spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 74(2)(2025), 277–293.
  15. Hossain, N., Mondal, R., Exploring generalized ideal convergence with Orlicz functions in neutrosophic n-normed spaces, J. Classical Anal., 26(2)(2025), 213–237.
  16. Jenifer, P.S., Jeyaraman, M., Jafari, S., Pigazzini, A., A study on rough ideal statistical convergence in neutrosophic normed spaces, Axioms, 14(9)(2025), 1–14.
  17. Karakaya, V., Şimşek, N., Ertürk, M., Gürsoy, F., Statistical convergence of sequences of functions in intuitionistic fuzzy normed spaces, Abstr. Appl. Anal., 2012(2012), 1–19.
  18. Karakaya, V., Şimşek, N., Ertürk, M., Gürsoy, F., λ-statistical convergence of sequences of functions in intuitionistic fuzzy normed spaces, J. Funct. Space, 2012(2012), 926193.
  19. Karakaya, V., Şimşek, N., Ertürk, M., Gürsoy, F., Lacunary statistical convergence of sequences of functions in intuitionistic fuzzy normed space, J. Intell. Fuzzy Syst., 26(2014), 1289–1299.
  20. Karakaya, V., Şimşek, N., Ertürk, M., Gürsoy, F., On ideal convergence of sequences of functions in intuitionistic fuzzy normed spaces, Appl. Math. Inf. Sci., 8(5)(2014), 2307–2313.
  21. Katsaras, A.K., Fuzzy topological vector spaces II, Fuzzy Sets Syst., 12(2)(1984), 143–154.
  22. Khan, V.A., Altaf, H., Alam, M., Ideal convergent sequences of functions in probabilistic normed spaces, J. Math. Computer Sci., 26(2022), 249–254.
  23. Khan, V.A., Esi, A., Ahmad, M., Khan, M.D., Continuous and bounded linear operators in neutrosophic normed spaces, J. Intell. Fuzzy Syst., 40(6)(2021), 11063–11070.
  24. Khan, V.A., Khan, M.D., Ahmad, M., Some new type of lacunary statistically convergent sequences in neutrosophic normed space, Neutrosophic Sets Syst., 42(2021), 239–252.
  25. Khan, V.A., Khan, M.D, Kumar, A., Statistical convergence of sequences of functions in neutrosophic normed spaces, Numer. Funct. Anal. Optim., 44(13)(2023), 1443–1463.
  26. Kirişci, M., Şimşek, N., Neutrosophic metric spaces, Math. Sci., 14(3)(2020), 241–248.
  27. Kirişci, M., Şimşek, N., Neutrosophic normed spaces and statistical convergence, J. Anal., 28(2020), 1059–1073.
  28. Kişi, Ö., Ideal convergence of sequences in neutrosophic normed spaces, J. Intell. Fuzzy Syst., 41(2)(2021), 2581–2590.
  29. Klement, E.P., Mesiar, R., Pap, E., Triangular norms. Position paper I: basic analytical and algebraic properties, Fuzzy Sets Syst., 143(2004), 5–26.
  30. Kostyrko, P., ˇ Sal´at, T., Wilczy´nski, W., I-convergence, Real Anal. Exchange, 26(2)(2000/2001), 669–685.
  31. Omran, S., Elrawy, A., Continuous and bounded operators on neutrosophic normed spaces, Neutrosophic Sets Syst., 46(20)(2021), 276–289.
  32. Park, J.H., Intutionistic fuzzy metric spaces, Chaos Solitons Fractals, 22(2004), 1039–1046.
  33. Riaz, M., Ishtiaq, U., Park, C., Ahmad, K., Uddin, F., Some fixed point results for ξ-chainable neutrosophic and generalized neutrosophic cone metric spaces with application, Aims Math., 7(8)(2022), 14756–14784.
  34. Saadati, R., Park, J.H., On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals, 27(2006), 331–344.
  35. Sal´at, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30(1980), 139–150.
  36. Sal´at, T., Tripathy, B.C., Ziman, M., On some properties of I-convergence, Tatra Mt. Math. Publ., 28(2)(2004), 279–286.
  37. Sal´at, T., Tripathy, B.C., Ziman, M., On I-convergence field, Ital. J. Pure Appl. Math., 17(5)(2005), 1–8.
  38. Savaş, E., Gürdal, M., Ideal convergent function sequences in random 2-normed spaces, Filomat, 22(1)(2025), 259–282.
  39. Schoenberg, I.J, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(5)(1959), 361–375.
  40. Schweizer, B., Sklar, A., Statistical metric spaces, Pacific J. Math., 10(1)(1960), 313–334.
  41. Shankar, H., Ahmad, A., Chaurasiya, C., Esi, A., λ-statistical pointwise and uniform convergence of sequences of functions on neutrosophic normed spaces, Sahand Commun. Math. Anal., 22(1)(2025), 259–282.
  42. Smarandache, F., Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure. Appl. Math., 24(2005), 287–297.
  43. Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2(1)(1951), 73–74.
  44. Zadeh, L.A., Fuzzy sets, Inform. Control, 8(1965), 338–353.
  45. Jenifer, P.S., Jeyaraman, M., Jafari, S., Pigazzini, A., A study on rough ideal statistical convergence in neutrosophic normed spaces, Axioms, 14(9)(2025), 1–14.
  46. Kişi, Ö., Ideal convergence of sequences in neutrosophic normed spaces, J. Intell. Fuzzy Syst., 41(2)(2021), 2581–2590.