Lacunary statistical harmonic summability. (English) Zbl 07885461
Summary: In this paper, the concepts of lacunary \((\mathrm{H}, 1)\) summability, lacunary strongly harmonically summability, lacunary statistical \((\mathrm{H}, 1)\) summability, lacunary statistical logarithmic convergence of sequences of real numbers are introduced and relations between these concepts are investigated.
MSC:
| 40D25 | Inclusion and equivalence theorems in summability theory |
| 40A05 | Convergence and divergence of series and sequences |
References:
| [1] | M. A. Alghamdi, M. Mursaleen and A. Alotaibi, Logarithmic density and loga-rithmic statistical convergence, Advances in Difference Equations, 2013, 2013, 227. · Zbl 1379.40001 |
| [2] | J. Connor, The statistical and strong p-Cesàro convergence of sequences, Anal-ysis, 1988, 8, 46-63. · Zbl 0653.40001 |
| [3] | J. Connor, On strong matrix summability with respect to a modulus and statis-tical convergence, Canad. Math. Bull., 1989, 32(2), 194-198. · Zbl 0693.40007 |
| [4] | O. H. H. Edely and M. Mursaleen, On statistical A-Cauchy and statistical A-summability via ideal, J. Inequal. Appl., 2021, 34. · Zbl 1504.40007 |
| [5] | H. Fast, Sur la convergence statistique, Colloq. Math., 1951, 2, 241-244. · Zbl 0044.33605 |
| [6] | A. R. Freedman, J. J. Sember and M. Raphael, Some Cesàro type summability spaces, Proc. London Math. Soc., 1978, 37, 508-520. · Zbl 0424.40008 |
| [7] | J. A. Fridy, On statistical convergence, Analysis, 1985, 5, 301-313. · Zbl 0588.40001 |
| [8] | J. A. Fridy and C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl., 1993, 173, 497-504. · Zbl 0786.40004 |
| [9] | J. A. Fridy and C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc., 1997, 125(12), 3625-3631. · Zbl 0883.40003 |
| [10] | D. Georgiou, A. Megaritis, G. Prinos and F. Sereti, On statistical convergence of sequences of closed sets in metric spaces, Mathematica Slovaca, 2021, 71(2), 409-422. · Zbl 1482.54005 |
| [11] | M. Işık and K. E. Et, On lacunary statistical convergence of order α in proba-bility, AIP Conference Proceedings, 2015, 1676, Article ID 020045. |
| [12] | M. Işık and K. E. Akbaş, On Asymptotically Lacunary Statistical Equivalent Sequences of Order α in Probability, ITM Web of Conferences, 2017, 13, Article ID 01024. DOI: 10.1051/itmconf/20171301024. · doi:10.1051/itmconf/20171301024 |
| [13] | V. Loku and N. L. Braha, A 2 -statistical convergence and its application to Ko-rovkin second theorem, Studia Universitatis Babes-Bolyai, Mathematica, 2019, (64)4, 537-549. · Zbl 1513.40064 |
| [14] | F. Móricz, Theorems relating to statistical harmonic summability and ordinary convergence of slowly decreasing or oscillating sequences, Analysis, 2004, 24, 127-145. · Zbl 1051.40006 |
| [15] | M. Mursaleen, S. Debnath and D. Rakshit, I-statistical limit superior and I-statistical limit inferior, Filomat, 2017, 31(7), 2103-2108. · Zbl 1488.40026 |
| [16] | S. A. Sezer, Statistical harmonic summability of sequences of fuzzy numbers, Soft. Comput., 2020. https://doi.org/10.1007/s00500-020-05151-9. · doi:10.1007/s00500-020-05151-9 |
| [17] | I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 1959, 66, 361-375. · Zbl 0089.04002 |
| [18] | H. M. Srivastava and M. Et, Lacunary statistical convergence and strongly lacunary summable function of order α, Filomat, 2017, 31(6), 1573-1582. · Zbl 1488.40034 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
