Geodesic
On $\mathcal{I}^{\mathcal{K}}$-convergence of sequences of bi-complex numbers
Problemy analiza, Tome 13 (2024) no. 3, pp. 43-55.

Voir la notice de l'article provenant de la source Math-Net.Ru

We propose the concept of $\mathcal{I}^{\mathcal{K}}$-convergence of sequences of bi-complex numbers. We explore the fundamental properties of this newly introduced notion and its relationships with other convergence methods.
Keywords: bi-complex number, ideal, filter, $\mathcal{I}$-convergence, $\mathcal{I}^*$-convergence, $\mathcal{I}^{\mathcal{K}}$-convergence. 
@article{PA_2024_13_3_a2,
     author = {J. Hossain and S. Debnath},
     title = {On $\mathcal{I}^{\mathcal{K}}$-convergence of sequences of bi-complex numbers},
     journal = {Problemy analiza},
     pages = {43--55},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2024_13_3_a2/}
}
TY  - JOUR
AU  - J. Hossain
AU  - S. Debnath
TI  - On $\mathcal{I}^{\mathcal{K}}$-convergence of sequences of bi-complex numbers
JO  - Problemy analiza
PY  - 2024
SP  - 43
EP  - 55
VL  - 13
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2024_13_3_a2/
LA  - en
ID  - PA_2024_13_3_a2
ER  - 
%0 Journal Article
%A J. Hossain
%A S. Debnath
%T On $\mathcal{I}^{\mathcal{K}}$-convergence of sequences of bi-complex numbers
%J Problemy analiza
%D 2024
%P 43-55
%V 13
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2024_13_3_a2/
%G en
%F PA_2024_13_3_a2
J. Hossain; S. Debnath. On $\mathcal{I}^{\mathcal{K}}$-convergence of sequences of bi-complex numbers. Problemy analiza, Tome 13 (2024) no. 3, pp. 43-55. http://geodesic.mathdoc.fr/item/PA_2024_13_3_a2/

[1] Bera S., Tripathy B. C., “Statistical convergence in a bi-complex valued metric space”, Ural Math. J., 9:1 (2023), 49–63 | DOI | MR

[2] Bera S., Tripathy B. C., “Statistical bounded sequences of bi-complex numbers”, Probl. Anal. Issues Anal., 12(30):2 (2023), 3–16 | DOI | MR | Zbl

[3] Choudhury C., Debnath S., “On $\mathcal{I}$-convergence of sequences in gradual normed linear spaces”, Facta. Univ. Ser. Math. Inform., 36:3 (2021), 595–604 | DOI | MR | Zbl

[4] Das P., Sleziak M., Toma V., “$\mathcal{I}^{\mathcal{K}}$- Cauchy functions”, Comp and Math with Appli., 173 (2014), 9–27 | DOI | MR | Zbl

[5] Debnath S., Choudhury C. On some properties of $\mathcal{I}^{K}$-convergence, Palest. J. Math., 11:2 (2022), 129–135 | MR | Zbl

[6] Debnath S., Rakshit D., “On $\mathcal{I}$-statistical convergence”, Iran. J. Math. Sci. Inform., 13:2 (2018), 101–109 | DOI | MR | Zbl

[7] Kostyrko P., Salat T., Wilczynski W., “$\mathcal{I}$-convergence”, Real. Anal. Exch., 26:2 (2000/2001), 669–686 | DOI | MR

[8] Macaj M., Sleziak M., “$\mathcal{I}^{\mathcal{K}}$-Convergence”, Real. Anal. Exch., 36 (2010–2011), 177–194 | DOI | MR

[9] Mursaleen M., Debnath S., Rakshit D., “$\mathcal{I}$-statistical limit superior and $\mathcal{I}$-statistical limit inferior”, Filomat, 31:7 (2017), 2103–2108 | DOI | MR | Zbl

[10] Nabiev A., Pehlivan S., Gurdal M., “On $\mathcal{I}$-Cauchy sequences”, Taiwanese J. Math., 11:2 (2007), 569–576 | DOI | MR | Zbl

[11] Price G. B., An Introduction to Multi-complex Spaces and Functions, Monographs and Text books in Pure and Applied Mathematics, Marcel Dekker. Inc., New York, 1991 | MR

[12] Rochon D., Shapiro M., “On algebraic properties of bi complex and hyperbolic numbers”, Anal. Univ. Oradea, Fasc. Math., 11 (2004), 71–110 | MR | Zbl

[13] Savas E., Das P., “A generalized statistical convergence via ideals”, Appl. Math. Lett., 24:6 (2011), 826–830 | DOI | MR | Zbl

[14] Scorza D. G., “Sulla rappresentazione delle funzioni di variabile bicomplessa totalmente derivabili”, Ann. Mat., 5 (1934), 597–665 | Zbl

[15] Segre C., “Le rappresentation reali delle forme complesse e gli enti iperalgebrici”, Math. Ann., 40 (1892), 413–467 (in Italian) | DOI | MR

[16] Spampinato N., “Estensione nel campo bicomplesso di due teoremi, del levi-Civita e del severi, per le funxione olomorfe di due variabili bicomplesse I, II”, Reale Accad. Naz. Lincei, 22:6 (1935), 96–102 | Zbl