A VARIATION ON LACUNARY STATISTICAL QUASI CAUCHY SEQUENCES

In this paper, the concept of a lacunary statistically -quasi-Cauchysequence is investigated. In this investigation, we proved interesting theoremsrelated to lacunary statisticallycontinuities. A real valued function f de…ned on a subset A of R, the set ofreal numbers, is called lacunary statisticallyserves lacunary statistically delta quasi-Cauchy sequences of points in A, i.e.(f (k))is a lacunary statistically delta quasi-Cauchy sequence whenever (k)is a lacunary statistically delta quasi-Cauchy sequence of points in A, wherea sequence (k)is called lacunary statistically delta quasi-Cauchy if (a lacunary statistically quasi-Cauchy sequence. It turns out that the set oflacunary statisticallyof continuous functions

Keywords:

Lacunary statistical convergence quasi-Cauchy sequences, continuity,

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Antoni, J., On the A-continuity of real functions II, Math. Slovaca (1986), 36 3, 283-287.
Buck, R.C., Solution of problem 4216, Amer. Math. Monthly (1948), 55, 36.
Burton, D. and Coleman, J., Quasi-Cauchy Sequences, Amer. Math. Monthly (2010), 117 4, 328-333.
Cakalli, H., Lacunary statistical convergence in topological groups, Indian J. Pure Appl.
Math. (1995), 26 2, 113-119.
Cakalli, H., Sequential de…nitions of compactness, Appl. Math. Lett. (2008), 21 6, 594-598.
Cakalli, H., Slowly oscillating continuity, Abstr. Appl. Anal. (2008), Hindawi Publ. Corp.
New York, ISSN 1085-3375 2008 Article ID 485706, 5 pages. ( doi:10.1155/2008/485706 ).
Cakalli, H., Forward continuity, J. Comput. Anal. Appl. (2011), 13 2, 225-230.
Cakalli, H., -quasi-Cauchy sequences, Math. Comput. Modelling (2011), 53(1-2), 397-401.
Cakalli, H., Statistical ward continuity, Appl. Math. Lett. (2011), 24 10, 1724-1728.
Cakalli, H., Statistical-quasi-Cauchy sequences, Math. Comput. Modelling (2011), 54 (5-6), 1620-1624.
Cakalli, H., Sequential de…nitions of connectedness, Appl. Math. Lett. (2012), 25 3, 461-465.
Cakalli, H., A Variation on Statistical Ward Continuity, Bull. Malays. Math. Sci. Soc. DOI 10.1007/s40840-015-0195-0
Cakalli, H., Aras, C.G., Sonmez, A., Lacunary statistical ward continuity, AIP Conf. Proc. (2015), 1676, 020042 http://dx.doi.org/10.1063/1.4930468
Çakalli, H. and Hazarika, B., Ideal Quasi-Cauchy sequences, J. Inequal. App (2012), 17 October, 2012. 2012:234 doi:10.1186/1029-242X-2012-234
Çakallı, H. and Das, Pratulananda, Fuzzy compactness via summability, Appl. Math. Lett. (2009), 22 11, 1665-1669.
Cakalli, H. and Kaplan, H., Strongly lacunary delta ward continuity, AIP Conference Pro- ceedings (2015), 1676, 020063 http://dx.doi.org/10.1063/1.4930489
Cakalli, H. and Khan, M.K., Summability in topological Spaces, Appl. Math. Lett. (2011), 24, 348-352.
Çakallı, H. and Savas, E., Statistical convergence of double sequences in topological groups, J. Comput. Anal. Appl. (2010), 12 2, 421-426.
Çakallı,H., Sönmez, A. and Genç, Ç, On an equivalence of topological vector space valued cone metric spaces and metric spaces, Appl. Math. Lett. (2012), 25 3, 429-433.
Connor, J. and Grosse-Erdmann, K.-G., Sequential de…nitions of continuity for real functions, Rocky Mountain J. Math. (2003), 33 1, 93-121.
Fast, H., Sur la convergence statistique, Colloq. Math. (1951), 2, 241-244.
Fridy, J.A., On statistical convergence, Analysis (1985), 5, 301-313.
Fridy, J.A. and Orhan, C., Lacunary statistical convergence, Paci…c J. Math. (1993), 160 1, 43-51.
Fridy, J.A. and Orhan, C., Lacunary statistical summability, J. Math. Anal. Appl (1993), 1732, 497-504
Keane, M., Understanding Ergodicity, Integers 11B (2011), 1-11.
Maio, G. Di and Kocinac, Ljubisa D.R., Statistical convergence in topology, Topology Appl. (2008), 156, 28-45.
Özgüç, I.S. and Yurdakadim, T., On quasi-statistical convergence, Commun. Fac. Sci. Univ. Ank. Series A1 (2012), 61 1, 11-17.
Öztürk, E., On almost-continuity and almost A-continuity of real functions, Comm.Fac.Sci. Univ.Ankara Ser. A1 Math. (1983), 32, 25-30.
Vallin, R.W., Creating slowly oscillating sequences and slowly oscillating continuous func- tions, With an appendix by Vallin and H. Cakalli. Acta Math. Univ. Comenianae (2011), 25 1, 71-78.
Winkler, P., Mathematical Puzzles: A Connoisseur’s Collection, A.K.Peters LTD (2004), ISBN 1-56881-201-9.
Current address : Huseyin Cakalli :Maltepe University,TR 34857, Maltepe, Istanbul, TURKEY
E-mail address : huseyincakalli@maltepe.edu.tr; hcakalli@gmail.com
Current address : Huseyin Kaplan: Nigde University, Department of Mathematics, Faculty of
Science and Letters, Nigde, TURKEY
E-mail address : hkaplan@nigde.edu.tr