Certain aspects of J-statistical supremum and J-statistical infimum of real-valued sequences

• Autorzy: Choudhury Chiranjib

Identyfikatory

DOI

10.1515/jaa-2022-1039

• Języki publikacji: EN

Abstrakty

EN

Over the last few years, numerous researchers have contributed significantly to summability theory by connecting various notions of convergence concepts of sequences. In this paper, we introduce the concepts of J-statistical supremum and J-statistical infimum of a real-valued sequence and study some fundamental features of the newly introduced notions.We also introduce the concept of J-statistical monotonicity and establish the condition under which an J-statistical monotonic sequence is J-statistical convergent. We end up giving a necessary and a sufficient condition for the J-statistical convergence of a real-valued sequence.

Słowa kluczowe

EN

ideal; filter; statistical convergence; J-statistical convergence; J-statistical supremum

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 2
• Strony: 305--312
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Choudhury Chiranjib

• Department of Mathematics, Tripura University (A Central University), Suryamaninagar-799022, Agartala, India

• https://orcid.org/0000-0002-5607-9884

Bibliografia

• [1] M. Altınok and M. Küçükaslan, A-statistical convergence and A-statistical monotonicity, Appl. Math. E-Notes 13 (2013), 249-260.
• [2] M. Altınok and M. Küçükaslan, A-statistical supremum-infimum and A-statistical convergence, Azerb. J. Math. 4 (2014), no. 2, 31-42.
• [3] M. Altınok and M. Küçükaslan, Ideal limit superior-inferior, Gazi Univ. J. Sci. 30 (2017), 401-411.
• [4] M. Altinok, M. Küçükaslan and U. Kaya, Statistical extension of bounded sequence space, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 70 (2021), no. 1, 82-99.
• [5] P. Das and E. Savas, On J-statistically pre-Cauchy sequences, Taiwanese J. Math. 18 (2014), no. 1, 115-126.
• [6] P. Das and E. Savas, On J-statistically pre-Cauchy sequences, Proyecciones 18 (2014), 115-126.
• [7] S. Debnath and C. Choudhury, On J-statistically ϕ-convergence, Proyecciones 40 (2021), no. 3, 593-604.
• [8] S. Debnath and D. Rakshit, On J-statistical convergence, Iran. J. Math. Sci. Inform. 13 (2018), no. 2, 101-109.
• [9] K. Demirci, I-limit superior and limit inferior, Math. Commun. 6 (2001), no. 2, 165-172.
• [10] K. Dems, On I-Cauchy sequences, Real Anal. Exchange 30 (2004/05), no. 1, 123-128.
• [11] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
• [12] J. A. Fridy, On statistical convergence, Analysis 5 (1985), no. 4, 301-313.
• [13] J. A. Fridy, Statistical limit points, Proc. Amer. Math. Soc. 118 (1993), no. 4, 1187-1192.
• [14] J. A. Fridy and C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (1997), no. 12, 3625-3631.
• [15] B. Hazarika and A. Esi, On asymptotically Wijsman lacunary statistical convergence of set sequences in ideal context, Filomat 31 (2017), no. 9, 2691-2703.
• [16] B. Hazarika and E. Savaş, λ-statistical convergence in n-normed spaces, An. Ştiinț. Univ. “Ovidius” Constanța Ser. Mat. 21 (2013), no. 2, 141-153.
• [17] P. Kostyrko, M. Mačaj, T. Šalát and M. Sleziak, I-convergence and extremal I-limit points, Math. Slovaca 55 (2005), no. 4, 443-464.
• [18] P. Kostyrko, T. Šalát and W. Wilczyński, I-convergence, Real Anal. Exchange 26 (2000/01), no. 2, 669-685.
• [19] M. Küçükaslan and M. Altinok, Statistical supremum-infimum and statistical convergence, Aligarh Bull. Math. 32 (2013), no. 1-2, 39-54.
• [20] P. Malik, A. Ghosh and S. Das, J-statistical limit points and J-statistical cluster points, Proyecciones 38 (2019), no. 5, 1011-1026.
• [21] S. A. Mohiuddine and B. Hazarika, Some classes of ideal convergent sequences and generalized difference matrix operator, Filomat 31 (2017), no. 6, 1827-1834.
• [22] S. A. Mohiuddine, B. Hazarika and M. A. Alghamdi, Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems, Filomat 33 (2019), no. 14, 4549-4560.
• [23] Mursaleen, λ-statistical convergence, Math. Slovaca 50 (2000), no. 1, 111-115.
• [24] M. Mursaleen, S. Debnath and D. Rakshit, On J-statistical limit superior and J-statistical limit inferior, Filomat 31 (2017), no. 7, 2103-2108.
• [25] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), no. 2, 139-150.
• [26] T. Šalát, B. C. Tripathy and M. Ziman, On some properties of I-convergence, Tatra Mt. Math. Publ. 28 (2004), 279-286.
• [27] E. Savas and P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett. 24 (2011), no. 6, 826-830.
• [28] E. Savaş and M. Gürdal, J-statistical convergence in probabilistic normed spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 77 (2015), no. 4, 195-204.
• [29] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73-74.
• [30] B. C. Tripathy, On statistically convergent and statistically bounded sequences, Bull. Malays. Math. Soc. (2) 20 (1997), no. 1, 31-33.
• [31] B. C. Tripathy, On statistically convergent sequences, Bull. Calcutta Math. Soc. 90 (1998), no. 4, 259-262.
• [32] B. C. Tripathy and B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca 59 (2009), no. 4, 485-494.
• [33] U. Yamancı and M. Gürdal, J-statistical convergence in 2-normed space, Arab J. Math. Sci. 20 (2014), no. 1, 41-47.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).