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Annals of the Alexandru Ioan Cuza University - Mathematics

The Journal of "Alexandru Ioan Cuza" University from Iasi

Editor-in-Chief: Oniciuc, Cezar

2 Issues per year


CiteScore 2016: 0.34

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.488

Mathematical Citation Quotient (MCQ) 2015: 0.10

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Online
ISSN
1221-8421
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λ-Almost Statistical Convergence of Order α

R. Çolak / Y. Altin / M. Et
Published Online: 2014-11-24 | DOI: https://doi.org/10.2478/aicu-2013-0041

Abstract

In this paper, we introduce the concept λ-almost statistical convergence of order α. Also some relations between λ-almost statistical convergence of order α and strong (V, λ)-almost summability of order α are given. Furthermore some relations between the space [Vαp, λ, f] and Ŝαλ are examined.

Keywords: statistical convergence; almost convergence; Cesaro summability

MSC: 40A05; 40C05; 46A45

References

  • 1. Banach, S. - Theorie des Operations Lineaires, Chelsea Publishing Co., New York, 1955.Google Scholar

  • 2. Colak, R.; Bektaş, C.A. - λ-statistical convergence of order α, Acta Math. Sci. Ser. B Engl. Ed., 31 (2011), 953-959.CrossrefGoogle Scholar

  • 3. Colak, R. - Statistical convergence of order α, Modern Methods in Analysis and Its Applications, NewDelhi, India, Anamaya Pub, 2010, 121-129.Google Scholar

  • 4. Colak, R.; Cakar, O. - Banach limits and related matrix transformations, Studia Sci. Math. Hungar., 24 (1989), 429-436.Google Scholar

  • 5. Connor, J.S. - The statistical and strong p-Cesaro convergence of sequences, Analysis, 8 (1988), 47-63.Google Scholar

  • 6. Duran, J.P. - Infinite matrices and almost-convergence, Math. Z., 128 (1972), 75-83.CrossrefGoogle Scholar

  • 7. Fast, H. - Sur la convergence statistique, Colloquium Math., 2 (1951), 241-244 (1952).Google Scholar

  • 8. Fridy, J.A. - On statistical convergence, Analysis, 5 (1985), 301-313.Google Scholar

  • 9. Gadjiev, A.D.; Orhan, C. - Some approximation theorems via statistical conver-gence, Rocky Mountain J. Math., 32 (2002), 129-138.Google Scholar

  • 10. King, J.P. - Almost summable sequences, Proc. Amer. Math. Soc, 17 (1966), 1219-1225.CrossrefGoogle Scholar

  • 11. Leindler, L. - Uber die verallgemeinerte de la Vallee-Poussinsche Summierbarkeit allgemeiner Orthogonalreihen, (German), Acta Math. Acad. Sci. Hungar., 16 (1965), 375-387.CrossrefGoogle Scholar

  • 12. Lorentz, G.G. - A contribution to the theory of divergent sequences, Acta Math., 80 (1948), 167-190.CrossrefGoogle Scholar

  • 13. Maddox, I.J. - Spaces of strongly summable sequences, Quart. J. Math. Oxford Ser., 18 (1967), 345-355.CrossrefGoogle Scholar

  • 14. Maddox, I.J. - Sequence spaces defined by a modulus, Math. Proc. Cambridge Philos. Soc, 100 (1986), 161-166.CrossrefGoogle Scholar

  • 15. Malkowsky, E.; Savas, E. - Some λ-sequence spaces defined by a modulus, Arch. Math. (Brno), 36 (2000), 219-228.Google Scholar

  • 16. Miller, H.I.; Orhan, C. - On almost convergent and statistically convergent sub-sequences, Acta Math. Hungar., 93 (2001), 135-151.CrossrefGoogle Scholar

  • 17. Mursaleen, M. - λ-statistical convergence, Math. Slovaca, 50 (2000), 111-115.Web of ScienceGoogle Scholar

  • 18. Mursaleen, M.; Alotaibi, A. - Statistical summability and approximation by de la Vallee-Poussin mean, Appl. Math. Lett., 24 (2011), 320-324.CrossrefWeb of ScienceGoogle Scholar

  • 19. Nakano, H. - Modular sequence spaces, Proc. Japan Acad, 27 (1953), 508-512.Google Scholar

  • 20. Rafi Segi Rahmat, M.; Lafuerza-Guillén, B. - Probabilistic norms and statistical convergence of random variables, Surv. Math. Appl., 4 (2009), 65-75.Google Scholar

  • 21. Rath, D.; Tripathy, B.C. - On statistically convergent and statistically Cauchy sequences, Indian J. Pure Appl. Math., 25 (1994), 381-386.Google Scholar

  • 22. Ruckle, W.H. - FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25 (1973), 973-978.CrossrefGoogle Scholar

  • 23. Šalát, T. - On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139-150.Google Scholar

  • 24. Savaş, E. - Strong almost convergence and almost λ-statistical convergence, Hokkaido Math. J., 29 (2000), 531-536.CrossrefGoogle Scholar

  • 25. Schoenberg, I.J. - The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361-375.CrossrefGoogle Scholar

  • 26. Steinhaus, H. - Sur la convergence ordinaire et la convergence asymptotique, Col-loquium Mathematicum, 2 (1951), 73-74.Google Scholar

  • 27. Zygmund, A. - Trigonometric Series, Cambridge University Press, Cambridge, UK, 1979.Google Scholar

About the article

Received: 2012-03-20

Revised: 2013-01-16

Accepted: 2013-03-04

Published Online: 2014-11-24


Citation Information: Annals of the Alexandru Ioan Cuza University - Mathematics, ISSN (Online) 1221-8421, DOI: https://doi.org/10.2478/aicu-2013-0041.

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© 2014 R. Çolak et. al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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