Abstract
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
Funding source: University Grants Commission
Award Identifier / Grant number: 16-6(DEC. 2018)/2019(NET/CSIR)
Funding statement: The author is also grateful to the University Grants Commission, India, for their fellowships funding under the UGC-SRF scheme (No. 16-6(DEC. 2018)/2019(NET/CSIR)) during the preparation of this paper.
Acknowledgements
The author thanks the anonymous referees for their constructive suggestions to improve the quality of the paper.
References
[1] M. Altınok and M. Küçükaslan, A-statistical convergence and A-statistical monotonicity, Appl. Math. E-Notes 13 (2013), 249–260. Search in Google Scholar
[2] M. Altınok and M. Küçükaslan, A-statistical supremum-infimum and A-statistical convergence, Azerb. J. Math. 4 (2014), no. 2, 31–42. Search in Google Scholar
[3] M. Altınok and M. Küçükaslan, Ideal limit superior-inferior, Gazi Univ. J. Sci. 30 (2017), 401–411. Search in Google Scholar
[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. 10.31801/cfsuasmas.736132Search in Google Scholar
[5]
P. Das and E. Savas,
On
[6]
P. Das and E. Savas,
On
[7]
S. Debnath and C. Choudhury,
On
[8]
S. Debnath and D. Rakshit,
On
[9] K. Demirci, I-limit superior and limit inferior, Math. Commun. 6 (2001), no. 2, 165–172. Search in Google Scholar
[10]
K. Dems,
On
[11] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244. 10.4064/cm-2-3-4-241-244Search in Google Scholar
[12] J. A. Fridy, On statistical convergence, Analysis 5 (1985), no. 4, 301–313. 10.1524/anly.1985.5.4.301Search in Google Scholar
[13] J. A. Fridy, Statistical limit points, Proc. Amer. Math. Soc. 118 (1993), no. 4, 1187–1192. 10.1090/S0002-9939-1993-1181163-6Search in Google Scholar
[14] J. A. Fridy and C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (1997), no. 12, 3625–3631. 10.1090/S0002-9939-97-04000-8Search in Google Scholar
[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. 10.2298/FIL1709691HSearch in Google Scholar
[16] B. Hazarika and E. Savaş, λ-statistical convergence in n-normed spaces, An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat. 21 (2013), no. 2, 141–153. 10.2478/auom-2013-0028Search in Google Scholar
[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. Search in Google Scholar
[18] P. Kostyrko, T. Šalát and W. Wilczyński, I-convergence, Real Anal. Exchange 26 (2000/01), no. 2, 669–685. 10.2307/44154069Search in Google Scholar
[19] M. Küçükaslan and M. Altinok, Statistical supremum-infimum and statistical convergence, Aligarh Bull. Math. 32 (2013), no. 1–2, 39–54. Search in Google Scholar
[20] P. Malik, A. Ghosh and S. Das, I-statistical limit points and I-statistical cluster points, Proyecciones 38 (2019), no. 5, 1011–1026. 10.22199/issn.0717-6279-2019-05-0065Search in Google Scholar
[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. 10.2298/FIL1706827MSearch in Google Scholar
[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. 10.2298/FIL1914549MSearch in Google Scholar
[23] Mursaleen, λ-statistical convergence, Math. Slovaca 50 (2000), no. 1, 111–115. Search in Google Scholar
[24]
M. Mursaleen, S. Debnath and D. Rakshit,
On
[25] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), no. 2, 139–150. Search in Google Scholar
[26]
T. Šalát, B. C. Tripathy and M. Ziman,
On some properties of
[27] E. Savas and P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett. 24 (2011), no. 6, 826–830. 10.1016/j.aml.2010.12.022Search in Google Scholar
[28]
E. Savaş and M. Gürdal,
[29] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73–74. 10.4064/cm-2-2-98-108Search in Google Scholar
[30] B. C. Tripathy, On statistically convergent and statistically bounded sequences, Bull. Malays. Math. Soc. (2) 20 (1997), no. 1, 31–33. Search in Google Scholar
[31] B. C. Tripathy, On statistically convergent sequences, Bull. Calcutta Math. Soc. 90 (1998), no. 4, 259–262. Search in Google Scholar
[32] B. C. Tripathy and B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca 59 (2009), no. 4, 485–494. 10.2478/s12175-009-0141-4Search in Google Scholar
[33]
U. Yamancı and M. Gürdal,
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Around the Świątkowski-type conditions
- Metamorphism—an integral transform reducing the order of a differential equation
- Linear isomorphic spaces of Cesàro–Nörlund operator, their duals and matrix transformations
- A generalized Suzuki–Berinde contraction that characterizes Banach spaces
- Asymptotic behavior of solutions toward the constant state to the Cauchy problem for the non-viscous diffusive dispersive conservation law
- Trigonometric Hermite interpolation method for Fredholm linear integral equations
- Smoothing Levenberg–Marquardt algorithm for solving non-Lipschitz absolute value equations
- Two-dimensional EMD with shape-preserving spline interpolation
- Computing subdifferential limits of operators on Banach spaces
- Certain aspects of ℐ-statistical supremum and ℐ-statistical infimum of real-valued sequences
- Weighted Simpson-like type inequalities for quasi-convex functions
- Bochner formula in generalized (k,μ)-space forms
- Convergence of a conjugate function in Zygmund space by almost Nörlund transform
- 2-point left Radau-type inequalities via s-convexity
- A general size-biased distribution
- A study of fuzzy anti-λ-ideal convergent triple sequence spaces
- Euler-type integrals for the generalized hypergeometric matrix function
- Korn’s inequality in anisotropic Sobolev spaces
Articles in the same Issue
- Frontmatter
- Around the Świątkowski-type conditions
- Metamorphism—an integral transform reducing the order of a differential equation
- Linear isomorphic spaces of Cesàro–Nörlund operator, their duals and matrix transformations
- A generalized Suzuki–Berinde contraction that characterizes Banach spaces
- Asymptotic behavior of solutions toward the constant state to the Cauchy problem for the non-viscous diffusive dispersive conservation law
- Trigonometric Hermite interpolation method for Fredholm linear integral equations
- Smoothing Levenberg–Marquardt algorithm for solving non-Lipschitz absolute value equations
- Two-dimensional EMD with shape-preserving spline interpolation
- Computing subdifferential limits of operators on Banach spaces
- Certain aspects of ℐ-statistical supremum and ℐ-statistical infimum of real-valued sequences
- Weighted Simpson-like type inequalities for quasi-convex functions
- Bochner formula in generalized (k,μ)-space forms
- Convergence of a conjugate function in Zygmund space by almost Nörlund transform
- 2-point left Radau-type inequalities via s-convexity
- A general size-biased distribution
- A study of fuzzy anti-λ-ideal convergent triple sequence spaces
- Euler-type integrals for the generalized hypergeometric matrix function
- Korn’s inequality in anisotropic Sobolev spaces