On deferred statistical convergence of sequences of sets

Mikail Et; M. Çagri Yilmazer; Mikail Et; M. Çagri Yilmazer

doi:10.3934/math.2020142

AIMS Mathematics

2020, Volume 5, Issue 3: 2143-2152. doi: 10.3934/math.2020142

Previous Article Next Article

Research article Special Issues

On deferred statistical convergence of sequences of sets

Mikail Et ^,,
M. Çagri Yilmazer

Department of Mathematics, Firat University, 23119 Elazıg, Turkey

Received: 10 December 2019 Accepted: 21 February 2020 Published: 27 February 2020
MSC : Primary: 40A05, 40C05; Secondary: 46A45

The main purpose of this paper is to introduce the concepts of Wijsman deferred statistical convergence and Wijsman strong deferred Cesàro summability for sequences of sets.
- deferred density,
- deferred Cesàro mean,
- statistical convergence,
- Wijsman convergence
Citation: Mikail Et, M. Çagri Yilmazer. On deferred statistical convergence of sequences of sets[J]. AIMS Mathematics, 2020, 5(3): 2143-2152. doi: 10.3934/math.2020142

Related Papers:

Abstract

The main purpose of this paper is to introduce the concepts of Wijsman deferred statistical convergence and Wijsman strong deferred Cesàro summability for sequences of sets.

References

[1]	H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244. doi: 10.4064/cm-2-3-4-241-244
[2]	H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951), 73-74.
[3]	V. K. Bhardwaj, S. Dhawan, Density by moduli and lacunary statistical convergence, Abstr. Appl. Anal., 2016 (2016), 9365037.
[4]	V. K. Bhardwaj, S. Dhawan, Density by moduli and Wijsman lacunary statistical convergence of sequences of sets, J. Inequal. Appl., 2017 (2017), 25.
[5]	H. Cakalli, Lacunary statistical convergence in topological groups, Indian J. Pure Appl. Math., 26 (1995), 113-119.
[6]	M. Cinar, M. Karakas, M. Et, On pointwise and uniform statistical convergence of order α for sequences of functions, Fixed Point Theory Appl., 2013 (2013), 33.
[7]	A. Caserta, G. Di Maio, L. D. R. Kočinac, Statistical convergence in function spaces, Abstr. Appl. Anal., 2011 (2011), 420419.
[8]	R. Colak, Statistical convergence of order α, In: Modern Methods in Analysis and Its Applications, Anamaya Pub, New Delhi, 2010, 121-129.
[9]	J. S. Connor, The statistical and strong p-Cesàro convergence of sequences, Analysis, 8 (1988), 47-63.
[10]	M. Et, B. C. Tripathy, A. J. Dutta, On pointwise statistical convergence of order α of sequences of fuzzy mappings, Kuwait J. Sci., 41 (2014), 17-30.
[11]	M. Et, R. Colak, Y. Altin, Strongly almost summable sequences of order α, Kuwait J. Sci., 41 (2014), 35-47.
[12]	M. Et, S. A. Mohiuddine, A. Alotaibi, On λ-statistical convergence and strongly λ-summable functions of order α, J. Inequal. Appl., 2013 (2013), 469.
[13]	A. Esi, N. L. Braha, A. Rushiti, Wijsman λ-statistical convergence of interval numbers, Bol. Soc. Parana. Mat., 35 (2017), 9-18.
[14]	J. Fridy, On statistical convergence, Analysis, 5 (1985), 301-313.
[15]	B. Hazarika, A. Esi, N. L. Braha, On asymptotically Wijsman lacunary σ-statistical convergence of set sequences, J. Math. Anal., 4 (2013), 33-46
[16]	M. Isik, K. E. Akbas, On λ-statistical convergence of order α in probability, J. Inequal. Spec. Funct., 8 (2017), 57-64.
[17]	M. Isik, K. E. Akbas, On asymptotically lacunary statistical equivalent sequences of order α in probability, ITM Web of Conferences, 13 (2017), 01024.
[18]	M. Mursaleen, λ- statistical convergence, Math. Slovaca, 50 (2000), 111-115.
[19]	F. Nuray, B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math., 49 (2012), 87-99.
[20]	T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139-150.
[21]	E. Savas, M. Et, On $(\Delta _{\lambda }^{m},I)-$statistical convergence of order α, Period. Math. Hungar., 71 (2015), 135-145. doi: 10.1007/s10998-015-0087-y
[22]	H. M. Srivastava, M. Et, Lacunary statistical convergence and strongly lacunary summable functions of order α, Filomat, 31 (2017), 1573-1582. doi: 10.2298/FIL1706573S
[23]	H. Sengul, M. Et, On I-lacunary statistical convergence of order α of sequences of sets, Filomat, 31 (2017), 2403-2412. doi: 10.2298/FIL1708403S
[24]	H. Sengul, On Wijsman I-lacunary statistical equivalence of order (η, μ), J. Inequal. Spec. Funct., 9 (2018), 92-101.
[25]	M. Yilmazturk, M. Kucukaslan, On strongly deferred Cesàro summability and deferred statistical convergence of the sequences, Bitlis Eren Univ. J. Sci. Technol., 3 (2011), 22-25.
[26]	R. P. Agnew, On deferred Cesàro means, Ann. Math., 33 (1932), 413-421. doi: 10.2307/1968524
[27]	M. Kucukaslan, M. Yilmazturk, On deferred statistical convergence of sequences, Kyungpook Math. J., 56 (2016), 357-366. doi: 10.5666/KMJ.2016.56.2.357

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)