Some Cesàro-type summability spaces defined by a modulus function of order (α;β)

Year 2017, Volume: 66 Issue: 2, 80 - 90, 01.08.2017

Hacer Şengül

https://doi.org/10.1501/Commua1_0000000803

Cited By: 15

Abstract

In this article, we introduce strong w [ ; f; p] summability of order (α;β) for sequences of complex (or real) numbers and give some inclusionrelations between the sets of lacunary statistical convergence of order (α;β) strong w [ ; f; p]summability and strong w (p)summability

Keywords

Lacunary sequence, modulus function, statistical convergence

References

• Altın, Y., Properties of some sets of sequences de…ned by a modulus function, Acta Math. Sci. Ser. B Engl. Ed. 29(2) (2009), 427–434.
• Caserta, A., Giuseppe, Di M. and Koµcinac, L. D. R., Statistical convergence in function spaces, Abstr. Appl. Anal. 2011, Art. ID 420419, 11 pp.
• Çakallı, H., A study on statistical convergence, Funct. Anal. Approx. Comput. 1(2) (2009), –24.
• Et, M., Generalized Cesàro diğerence sequence spaces of non-absolute type involving lacunary sequences, Appl. Math. Comput. 219(17) (2013), 9372–9376.
• Gadjiev, A. D., and Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32(1) (2002), 129-138.
• Kolk, E., The statistical convergence in Banach spaces, Acta Comment. Univ. Tartu, 928 (1991), 41-52.
• Çolak, R., Statistical convergence of order ;Modern Methods in Analysis and Its Applica- tions, New Delhi, India: Anamaya Pub, 2010: 121–129.
• Connor, J. S., The Statistical and Strong p-Cesaro Convergence of Sequences, Analysis,8, pp. (1988), 47-63.
• Fast, H., Sur La Convergence Statistique, Colloq. Math., 2, pp. (1951), 241–244.
• Fridy, J., On Statistical Convergence, Analysis, 5, pp. (1985), 301-313.
• Fridy, J., and Orhan, C., Lacunary Statistical Convergence, Paci…c J. Math., 160, pp. (1993), –51.
• Fridy, J., and Orhan, C., Lacunary Statistical Summability, J. Math. Anal. Appl., 173, pp. (1993), no. 2, 497–504.
• Schoenberg, I. J., The Integrability of Certain Functions and Related Summability Methods, Amer. Math. Monthly, 66, pp. (1959), 361–375.
• Salat, T., On Statistically Convergent Sequences of Real Numbers, Math. Slovaca., 30, pp. (1980), 139-150.
• Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951) 73-74.
• ¸Sengül, H., On Statistical Convergence of Order ( ; ) : (In rewiev) Et, M., and ¸Sengül, H., Some Cesaro-type summability spaces of order and lacunary statistical convergence of order , Filomat 28 (2014), no. 8, 1593–1602.
• ¸Sengül, H., and Et, M., On lacunary statistical convergence of order , Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 2, 473–482.
• Pehlivan, S., and Fisher, B., Some sequence spaces de…ned by a modulus, Mathematica Slovaca vol. 45, no. 3, pp. 275–280,1995.
• Nakano, H., Modulared sequence spaces, Proc. Japan Acad. 27 (1951), 508–512.
• Gaur, A. K., and Mursaleen, M., Diğerence sequence spaces de…ned by a sequence of moduli, Demonstratio Math. 31(2) (1998), 275–278.
• Nuray, F., and Sava¸s, E., Some new sequence spaces de…ned by a modulus function, Indian J. Pure Appl. Math. 24(11) (1993), 657–663.
• I¸sık, M., Strongly almost (w; ; q) summable sequences, Math. Slovaca 61(5) (2011), 779–
• Maddox, I. J., Elements of Functional Analysis, Cambridge University Press, 1970.
• Maddox, I. J., Sequence spaces de…ned by a modulus, Math. Proc. Camb. Philos. Soc, 1986, :161-166.
• Et, M., Strongly almost summable diğerence sequences of order m de…ned by a modulus, Studia Sci. Math. Hungar. 40(4) (2003), 463–476.
• Et, M., Spaces of Cesàro diğerence sequences of order r de…ned by a modulus function in a locally convex space, Taiwanese J. Math. 10(4) (2006), 865-879.
• Ruckle, W. H., FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math. 25 (1973), 973–978.
• Pehlivan, S. and Fisher, B., Lacunary strong convergence with respect to a sequence of modulus functions, Comment. Math. Univ. Carolin. 36 (1995), no. 1, 69-76.