Generalized statistically pre-Cauchy triple sequences via Orlicz functions
Journal of nonlinear sciences and its applications, Tome 14 (2021) no. 6, p. 414-422.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this study, we tried to construct $\mathcal{I}$-statistically pre-Cauchy on triple sequences via Orlicz functions $\widetilde{\phi}$. We prove that for triple sequences, $\mathcal{I}$-statistical $\widetilde{\phi}$-convergence implies $\mathcal{I}$-statistical pre-Cauchy condition and examine some main properties of these concepts.
DOI : 10.22436/jnsa.014.06.04
Classification : 40A35, 40D25
Keywords: \(\mathcal{I}\)-statistical convergence, \(\mathcal{I}\)-statistical pre-Cauchy, triple sequences, Orlicz function

Huban, Mualla Birgul  1

1 Isparta University of Applied Sciences, Isparta, Turkey
@article{JNSA_2021_14_6_a3,
     author = {Huban, Mualla Birgul },
     title = {Generalized statistically {pre-Cauchy} triple sequences via {Orlicz} functions},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {414-422},
     publisher = {mathdoc},
     volume = {14},
     number = {6},
     year = {2021},
     doi = {10.22436/jnsa.014.06.04},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.014.06.04/}
}
TY  - JOUR
AU  - Huban, Mualla Birgul 
TI  - Generalized statistically pre-Cauchy triple sequences via Orlicz functions
JO  - Journal of nonlinear sciences and its applications
PY  - 2021
SP  - 414
EP  - 422
VL  - 14
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.014.06.04/
DO  - 10.22436/jnsa.014.06.04
LA  - en
ID  - JNSA_2021_14_6_a3
ER  - 
%0 Journal Article
%A Huban, Mualla Birgul 
%T Generalized statistically pre-Cauchy triple sequences via Orlicz functions
%J Journal of nonlinear sciences and its applications
%D 2021
%P 414-422
%V 14
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.014.06.04/
%R 10.22436/jnsa.014.06.04
%G en
%F JNSA_2021_14_6_a3
Huban, Mualla Birgul . Generalized statistically pre-Cauchy triple sequences via Orlicz functions. Journal of nonlinear sciences and its applications, Tome 14 (2021) no. 6, p. 414-422. doi : 10.22436/jnsa.014.06.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.014.06.04/

[1] Connor, J.; Fridy, J.; Kline, J. Statistically pre-Cauchy sequences, Analysis, Volume 14 (1994), pp. 311-317 | DOI

[2] Das, P.; Ghosal, S. K. Some further results on I-Cauchy sequences and condition (AP), Comput. Math. Appl.,, Volume 59 (2010), pp. 2597-2600 | DOI

[3] Das, P.; Savas, E. ON I-STATISTICALLY PRE-CAUCHY SEQUENCES, Taiwanese J. Math., Volume 18 (2014), pp. 115-126

[4] Das, P.; Savas¸, E.; Ghosal, S. K. On generalizations of certain summability methods using ideals, Appl. Math. Lett., Volume 24 (2011), pp. 1509-1514 | DOI

[5] Demirci, K. I-limit superior and limit inferior, Math. Commun, Volume 6 (2001), pp. 165-172

[6] Esi, A.; Subramanian, N. On triple sequence spaces of $X^3$, World Sci. News, Volume 95 (2018), pp. 159-166

[7] Esi, A.; Subramanian, N.; Esi, A. On triple sequence space of Bernstein operator of rough I-convergence pre-Cauchy sequences, Proyecciones, Volume 36 (2017), pp. 567-587 | DOI

[8] Fast, H. Sur la convergence statistique, Colloq. Math., Volume 2 (1951), pp. 241-244 | DOI

[9] Freedman, A. R.; Sember, J. J. Densities and summability, Pacific J. Math., Volume 95 (1981), pp. 293-305

[10] Fridy, J. A. On statistical convergence, Analysis, Volume 5 (1985), pp. 301-313 | DOI

[11] Gurdal, M. SStatistically pre-Cauchy sequences and bounded moduli, Acta Comment. Univ. Tartu. Math., Volume 7 (2003), pp. 3-7

[12] Gurdal, M. Some types of convergence, Doctoral Diss, S. Demirel Univ., Isparta, 2004

[13] Gurdal, M.; Acık, I. On I-Cauchy sequences in 2-normed spaces, Math. Inequal. Appl., Volume 11 (2008), pp. 349-354 | DOI

[14] Gurdal, M.; Sahiner, A. Extremal I-limit points of double sequences, Appl. Math. E-Notes, Volume 8 (2008), pp. 131-137

[15] Gurdal, M.; Huban, M. B. On I-convergence of double sequences in the topology induced by random 2-norms, Mat. Vesnik,, Volume 66 (2014), pp. 73-83 | EuDML

[16] Gurdal, M.; Huban, M. B. Statistical convergence and $C^∗$-operator algebras, Theory Appl. Math. Comput. Sci., Volume 7 (2017), pp. 41-50

[17] Hazarika, B.; Esi, A. Lacunary ideal quasi Cauchy sequences, An. Univ. Craiova Ser. Mat. Inform., Volume 45 (2018), pp. 220-231

[18] Hazarika, B.; Subramanian, N.; Mursaleen, M. Korovkin-type approximation theorem for Bernstein operator of rough statistical convergence of triple sequences, Adv. Oper. Theory, Volume 5 (2020), pp. 324-335 | DOI

[19] Huban, M. B.; Gurdal, M. Wijsman lacunary invariant statistical convergence for triple sequences via Orlicz function, J. Classical Anal., Volume 2021 (2021)

[20] Huban, M. B.; Gurdal, M.; Bayturk, H. On asymptotically lacunary statistical equivalent triple sequences via ideals and Orlicz function, Honam Math. J., Volume 2021 (2021)

[21] Huban, M. B.; Gurdal, M.; Savas, E. I-statistical limit superior and I-statistical limit inferior of triple sequences, 7th International Conference on Recent Advances in Pure and Applied Mathematics, Proceeding Book of ICRAPAM, Volume 2020 (2020), pp. 42-49

[22] Indumathi, A.; Subramanian, N.; Hazarika, B. On the Borel summability method for convergence of triple sequences of Bernstein-Stancu operators of fuzzy numbers, Soft Comput., Volume 25 (2021), pp. 683-697 | DOI

[23] Khan, V. A.; Khan, N.; Esi, A.; Tabassum, T. I-pre-Cauchy double sequences and Orlicz functions, Engineering, Volume 5 (2013), pp. 52-56

[24] Kostyrko, P.; Salat, T.; Wilczynski, W. I-convergence, Real Anal. Exchange, Volume 26 (2000-2001), pp. 669-685 | DOI

[25] Malik, P.; Ghosh, A.; Maity, M. Strongly I and $I^∗$-statistically pre-Cauchy double sequences in probabilistic metric spaces, Mat. Vesnik, Volume 2 (2018), pp. 97-109

[26] Nabiev, A.; Pehlivan, S.; Gurdal, M. On I-Cauchy sequences, Taiwanese J. Math., Volume 11 (2007), pp. 569-576

[27] Raj, K .; Esi, A.; Jamwal, S. Orlicz-Quasi-Cauchy double sequence spaces for RH-regular matrix, J. Class. Anal., Volume 10 (2017), pp. 67-76 | DOI

[28] Rao, M. M.; Ren, Z. D. Applications of Orlicz spaces, Marcel Dekker, Marcel Dekker, 2002

[29] S¸ahiner, A.; Gurdal, M. New sequence spaces in n-normed spaces with respect to an Orlicz function, Aligarh Bull. Maths, Volume 27 (2008), pp. 53-58

[30] S¸ahiner, A.; Gurdal, M.; Duden, F. K. Triple sequences and their statistical convergence, Selc¸uk J. Appl. Math., Volume 8 (2007), pp. 49-55

[31] S¸ahiner, A.; Gurdal, M.; Saltan, S.; Gunawan, H. Ideal convergence in 2-normed spaces, Taiwanese J. Math., Volume 11 (2007), pp. 1477-1484

[32] S¸ahiner, A.; Gurdal, M.; Yigit, T. Ideal convergence characterization of the completion of linear n-normed spaces, Comput. Math. Appl., Volume 61 (2011), pp. 683-689 | DOI

[33] Sahiner, A.; Tripathy, B. C. Some I-related Properties of Triple Sequence, Selc¸uk J. Appl. Math., Volume 9 (2008), pp. 9-18

[34] Salat, T. On statistically convergent sequences of real numbers, Math. Slovaca, Volume 30 (1980), pp. 139-150

[35] Salat, T.; Tripathy, B. C.; Ziman, M. On some properties of I-convergence, Tatra Mt. Math. Publ., Volume 28 (2004), pp. 279-286

[36] Savas, R. Multiple λµ-statistically convergence via φe-functions, Math. Methods Appl. Sci., Volume 2020 (2020), pp. 1-8

[37] Savas¸, E.; Das, P. A generalized statistical convergence via ideals, Appl. Math. Lett., Volume 24 (2011), pp. 826-830 | DOI

[38] Savas, E.; Gurdal, M. Generalized statistically convergent sequences of functions in fuzzy 2-normed spaces, J. Intell. Fuzzy Syst., Volume 27 (2014), pp. 2067-2075 | DOI

[39] Savas, E.; Gurdal, M. A generalized statistical convergence in intuitionistic fuzzy normed spaces, ScienceAsia, Volume 41 (2015), pp. 289-294

[40] Schoenberg, I. J. The integrability of certain functions and related sumability methods, Amer. Math. Monthly, Volume 66 (1959), pp. 361-375 | DOI

[41] Steinhaus, H. Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., Volume 2 (1951), pp. 73-74

[42] Yamancı, U.; Gurdal, M. I-statistical convergence in 2-normed space, Arab J. Math. Sci., Volume 20 (2014), pp. 41-47 | DOI

[43] Yamancı, U.; Gurdal, M. I -statistically pre-Cauchy double sequences, Glob. J. Math. Anal., Volume 2 (2014), pp. 297-303

[44] Zygmund, A. Trigonometric Series, Cambridge Univ. Press, Cambridge, 1979

Cité par Sources :