Abstract
In this paper, we introduce and study \(\mathcal{I}\)-lacunary statistical convergence of order α in topological groups and we shall also present some inclusion theorems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
H. Albayrak and S. Pehlivan, Statistical convergence and statistical continuity on locally solid Riesz spaces, Topology Appl. 159, 1887–1893 (2012)
H. Çakalli, On Statistical Convergence in topological groups, Pure and Appl. Math. Sci. 43, No. 1-2, 27–31 (1996)
H. Çakalli-, Lacunary statistical convergence in topological groups, Indian J. Pure Appl. Math. 26, (2), 113–119 (1995)
R. Colak, Statistical convergence of order α, Modern methods in Analysis and its Applications, New Delhi, India, Anamaya Pub. 121–129 (2010)
P. Das and E. Savaş, S. K. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Letters. 24, 1509–1514 (2011)
P. Das, E. Savaş, On \(\mathcal{I}\)-convergence of nets in locally solid Riesz spaces, Filomat. 27:1, 84–89 (2013)
P. Das and E. Savaş, On \(\mathcal{I}\)-statistical and \(\mathcal{I}\)-lacunary statistical convergence of order α, Bull. Iranian Math. Soc. (Preprint)
P. Das and E. Savaş, On \(\mathcal{I}_{\lambda }\)-statistical convergence in locally solid Riesz spaces, Math. Slovaca (Preprint)
H. Fast, Sur la convergence statistique, Colloq Math. 2, 241–244 (1951)
J. A. Fridy, On ststistical convergence, Analysis. 5, 301–313 (1985)
J. A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160, 43–51 (1993)
A. D. Gadjiev and C. Orhan, some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32(1), 508–520 (2002)
P. Kostyrko, T. Šalát, W.Wilczynki, \(\mathcal{I}\)-convergence, Real Anal. Exchange. 26 (2), 669–685 (2000/2001)
P. Kostyrko, M. Macaj, T. Šalát, and M. Sleziak, \(\mathcal{I}\)-convergence and extremal \(\mathcal{I}\)-limit points, Math. Slovaca. 55, 443–464 (2005)
B.K. Lahiri and Pratulananda Das, On \(\mathcal{I}\) and \(\mathcal{I}{\ast}\) convergence of nets, Real Anal.Exchange, 33(2), 431–442 (2007–2008)
I. J Maddox, Statistical convergence in locally convex spaces, Math Proc. Camb. Phil. Soc. 104, 141–145 (1988)
G. D. Maio and L. D. R. Kocinac, Statistical convergence in topology, Topology Appl. 156, 28–45 (2008)
M. Mursaleen and S. A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, Journal of Computational and Applied Mathematics. 233(2), 142–149 (2009)
T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca. 30, 139–150 (1980)
E. Savaş and Pratulananda Das, A generalized statistical convergence via ideals, Appl. Math. Lett. 24, 826–830 (2011)
E. Savaş, Δ m-strongly summable sequence spaces in 2-normed spaces defined by ideal convergence and an Orlicz function, Appl. Math. Comput. 217 271–276 (2010)
E. Savaş, A sequence spaces in 2-normed space defined by ideal convergence and an Orlicz function, Abst. Appl. Anal., Vol. (2011), Article ID 741382
E. Savaş, On some new sequence spaces in 2-normed spaces using Ideal convergence and an Orlicz function, J. Ineq. Appl. Article Number: 482392 DOI: 10.1155/2010/482392 Published: (2010)
E. Savaş, On generalized double statistical convergence via ideals, The Fifth Saudi Science Conference,16–18 April (2012)
E. Savaş and Pratulananda Das, A generalized statistical convergence via ideals, Appl. Math. Letters. 24, 826–830 (2011)
E. Savaş, On Lacunary double statistical convergence in locally solid Riesz spaces J. Ineq. Appl. (2013)
E. Savaş, \(\mathcal{I}_{\theta }\) -statistically convergent sequences in topological groups, the Revista de la Unión Matemática Argentina. (Preprint)
I.J. Schoenberg, The integrability methods, Amer. Math. Monthly. 66, 361–375 (1959)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Savaş, E., Eren, R.S. (2015). \(\mathcal{I}_{\theta }\)-statistical convergence of order α in topological groups. In: Jeribi, A., Hammami, M., Masmoudi, A. (eds) Applied Mathematics in Tunisia. Springer Proceedings in Mathematics & Statistics, vol 131. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-18041-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-18041-0_6
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-18040-3
Online ISBN: 978-3-319-18041-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)