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

Ömer Kişi; Dr. Nesar Hossain; Carlos Granados

doi:10.47000/tjmcs.1815791

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

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.

Keywords

References

Antal, R., Chawla, M., Some aspects of λ-Δm-statistical convergence on neutrosophic normed spaces, Kyungpook Math. J., 64(3)(2024), 461–478.
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.
Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20(1986), 87–96.
Bilgin, N.G., Hilbert I-statistical convergence on neutrosophic normed spaces, Gazi Univ. J. Sci. Part A: Eng. Innov., 10(1)(2023), 1–8.
Bilgin, N.G., Arithmetic statistically convergent on neutrosophic normed spaces, G¨um¨us¸hane Univ. J. Sci., 13(2)(2023), 270–280.
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.
Chawla, M., Antal, R., Kaur, M., Rough λ-statistical convergence in neutrosophic normed spaces, Honam Math. J., 47(2)(2025), 141–158.
Connor, J.S., The statistical and strong p–Ces`aro convergence of sequences, Analysis, 8(1988), 47–63.

Fast, H., Sur la convergence statistique, Colloq. Math., 2(3-4)(1951), 241–244.
Felbin, C., Finite dimensional fuzzy normed linear space, Fuzzy Sets Syst., 48(2)(1992), 239–248.
Fridy, J.A., On statistical convergence, Analysis, 5(1985), 301–313.
George, A., Veeramani, P., On some results in fuzzy metric spaces, Fuzzy Sets Syst., 64(1994), 395–399.
Granados, C., Choudhury, C., Quasi statistical convergence in neutrosophic normed spaces for triple sequence spaces, Asian-Eur. J. Math., 16(03)(2023), 2350034.
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.
Hossain, N., Mondal, R., Exploring generalized ideal convergence with Orlicz functions in neutrosophic n-normed spaces, J. Classical Anal., 26(2)(2025), 213–237.
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.
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.
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.
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.
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.
Katsaras, A.K., Fuzzy topological vector spaces II, Fuzzy Sets Syst., 12(2)(1984), 143–154.
Khan, V.A., Altaf, H., Alam, M., Ideal convergent sequences of functions in probabilistic normed spaces, J. Math. Computer Sci., 26(2022), 249–254.
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.
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.
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.
Kirişci, M., Şimşek, N., Neutrosophic metric spaces, Math. Sci., 14(3)(2020), 241–248.
Kirişci, M., Şimşek, N., Neutrosophic normed spaces and statistical convergence, J. Anal., 28(2020), 1059–1073.
Kişi, Ö ., Ideal convergence of sequences in neutrosophic normed spaces, J. Intell. Fuzzy Syst., 41(2)(2021), 2581–2590.
Klement, E.P., Mesiar, R., Pap, E., Triangular norms. Position paper I: basic analytical and algebraic properties, Fuzzy Sets Syst., 143(2004), 5–26.
Kostyrko, P., ˇ Sal´at, T., Wilczy´nski, W., I-convergence, Real Anal. Exchange, 26(2)(2000/2001), 669–685.
Omran, S., Elrawy, A., Continuous and bounded operators on neutrosophic normed spaces, Neutrosophic Sets Syst., 46(20)(2021), 276–289.
Park, J.H., Intutionistic fuzzy metric spaces, Chaos Solitons Fractals, 22(2004), 1039–1046.
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.
Saadati, R., Park, J.H., On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals, 27(2006), 331–344.
Sal´at, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30(1980), 139–150.
Sal´at, T., Tripathy, B.C., Ziman, M., On some properties of I-convergence, Tatra Mt. Math. Publ., 28(2)(2004), 279–286.
Sal´at, T., Tripathy, B.C., Ziman, M., On I-convergence field, Ital. J. Pure Appl. Math., 17(5)(2005), 1–8.
Savaş, E., Gürdal, M., Ideal convergent function sequences in random 2-normed spaces, Filomat, 22(1)(2025), 259–282.
Schoenberg, I.J, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(5)(1959), 361–375.
Schweizer, B., Sklar, A., Statistical metric spaces, Pacific J. Math., 10(1)(1960), 313–334.
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.
Smarandache, F., Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure. Appl. Math., 24(2005), 287–297.
Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2(1)(1951), 73–74.
Zadeh, L.A., Fuzzy sets, Inform. Control, 8(1965), 338–353.

Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis

Journal Section

Research Article

Authors

Ömer Kişi ^*
0000-0001-6844-3092
Türkiye

Dr. Nesar Hossain
0000-0002-2205-3344
India

Carlos Granados
0000-0002-7754-1468
Colombia

Publication Date

June 30, 2026

Submission Date

November 2, 2025

Acceptance Date

February 6, 2026

Published in Issue

Year 2026 Volume: 18 Number: 2

DOI

https://doi.org/10.47000/tjmcs.1815791

IZ

https://izlik.org/JA88US53AT

Cite

RIS / Bibtex

APA

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, 18(2), 384-395. https://doi.org/10.47000/tjmcs.1815791

AMA

1.Kişi Ö, Hossain DN, Granados C. Recent Advances in the Convergence of Function Sequences in Neutrosophic Normed Spaces via Ideals. TJMCS. 2026;18(2):384-395. doi:10.47000/tjmcs.1815791

Chicago

Kişi, Ömer, Dr. Nesar Hossain, and Carlos Granados. 2026. “Recent Advances in the Convergence of Function Sequences in Neutrosophic Normed Spaces via Ideals”. Turkish Journal of Mathematics and Computer Science 18 (2): 384-95. https://doi.org/10.47000/tjmcs.1815791.

EndNote

Kişi Ö, Hossain DN, Granados C (June 1, 2026) Recent Advances in the Convergence of Function Sequences in Neutrosophic Normed Spaces via Ideals. Turkish Journal of Mathematics and Computer Science 18 2 384–395.

IEEE

[1]Ö. Kişi, D. N. Hossain, and C. Granados, “Recent Advances in the Convergence of Function Sequences in Neutrosophic Normed Spaces via Ideals”, TJMCS, vol. 18, no. 2, pp. 384–395, June 2026, doi: 10.47000/tjmcs.1815791.

ISNAD

Kişi, Ömer - Hossain, Dr. Nesar - Granados, Carlos. “Recent Advances in the Convergence of Function Sequences in Neutrosophic Normed Spaces via Ideals”. Turkish Journal of Mathematics and Computer Science 18/2 (June 1, 2026): 384-395. https://doi.org/10.47000/tjmcs.1815791.

JAMA

1.Kişi Ö, Hossain DN, Granados C. Recent Advances in the Convergence of Function Sequences in Neutrosophic Normed Spaces via Ideals. TJMCS. 2026;18:384–395.

MLA

Kişi, Ömer, et al. “Recent Advances in the Convergence of Function Sequences in Neutrosophic Normed Spaces via Ideals”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 2, June 2026, pp. 384-95, doi:10.47000/tjmcs.1815791.

Vancouver

1.Ömer Kişi, Dr. Nesar Hossain, Carlos Granados. Recent Advances in the Convergence of Function Sequences in Neutrosophic Normed Spaces via Ideals. TJMCS. 2026 Jun. 1;18(2):384-95. doi:10.47000/tjmcs.1815791