Skip to main content
SpringerLink
Log in

An Extension Asymptotically \(\lambda \)-Statistical Equivalent Sequences via Ideals

  • Conference paper
  • First Online:
Mathematics and Computing (ICMC 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 253))

Included in the following conference series:

  • 621 Accesses

Abstract

In (Savaş in Indian J Math 56(2):1–10 (2014) [27]), we examine the asymptotically \(\mathcal {I}^{\lambda }\)-statistical equivalent of order \(\alpha \) which is a natural combination of the definition for asymptotically equivalent of order \(\alpha \), where \(0 < \alpha \le 1\), \(\mathcal {I}\)-statistically limit, and \(\lambda \)-statistical convergence. In this paper, we continue to study by proving some more results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bhunia, S., Das, P., Pal, S.: Restricting statistical convergenge. Acta Math. Hungar 134(1–2), 153–161 (2012)

    Article  MathSciNet  Google Scholar 

  2. Colak, R.: Statistical Convergence of Order \(\alpha \), Modern Methods in Analysis and its Applications, pp. 121–129. Anamaya Publishers, New Delhi (2010)

    Google Scholar 

  3. Colak, R., Bektas, C.A.: \(\lambda \)-statistical convergence of order \(\alpha \). Acta Math. Scientia 31B(3), 953–959 (2011)

    Article  MathSciNet  Google Scholar 

  4. Das, P., Savaş, E.: On \(\cal{I}\)-statistical and \( \cal{I}\)-lacunary statistical convergence of order \(\alpha \). Bull. Iranian Soc. 40(2), 459–472 (2014)

    MathSciNet  MATH  Google Scholar 

  5. Et, M., Çınar, M., Karakaş, M.: On \(\lambda \)-statistical convergence of order \(\alpha \) of sequences of function. J. Inequal. Appl. 2013, 204 (2013)

    Article  MathSciNet  Google Scholar 

  6. Gumus, H., Savas, E.: On \(S_{\lambda }^{L}(\cal{I})\)-asymptotically statistical equivalent sequences. Numer. Analy. Appl. Math. (ICNAAM: AIP conference proceeding, vol. 1479 (2012) pp. 936–941 (2012)

    Google Scholar 

  7. Fast, H.: Sur la convergence statistique. Colloq. Math. 2, 241–244 (1951)

    Article  MathSciNet  Google Scholar 

  8. Fridy, J.A.: On statistical convergence. Analysis 5, 301–313 (1985)

    Article  MathSciNet  Google Scholar 

  9. Kolk, E.: The statistical convergence in Banach spaces. Acta Comment. Univ. Tartu 928, 41–52 (1991)

    MathSciNet  Google Scholar 

  10. Kostyrko, P., Šalát, T., Wilczynki, W.: \(\cal{I}\)-convergence. Real Anal. Exchange 26(2) 669–685 (2000/2001)

    Google Scholar 

  11. Kumar, V., Sharma, A.: On asymptotically generalized statistical equivalent sequences via ideal. Tamkang J. Math. 43(3), 469–478 (2012)

    MathSciNet  MATH  Google Scholar 

  12. Li, J.: Asymptotic equivalence of sequences and summability. Int. J. Math. Math. Sci. 20(4), 749–758 (1997)

    Article  MathSciNet  Google Scholar 

  13. Marouf, M.: Asymptotic equivalence and summability. Int. J. Math. Math. Sci. 16(4), 755–762 (1993)

    Article  MathSciNet  Google Scholar 

  14. Mursaleen, M.: \(\lambda \)-statistical convergence. Math. Slovaca 50, 111–115 (2000)

    MathSciNet  MATH  Google Scholar 

  15. Nuray, F., Ruckle, W.H.: Generalized statistical convergence and convergence free spaces. J. Math. Anal. Appl. 245(2), 513–527 (2000)

    Article  MathSciNet  Google Scholar 

  16. Patterson, R.F.: On asymptotically statistically equivalent sequences. Demonstratio Math. 36(1), 149–153 (2003)

    MathSciNet  MATH  Google Scholar 

  17. Šalát, T.: On statistically convergent sequences of real numbers. Math. Slovaca 30, 139–150 (1980)

    MathSciNet  MATH  Google Scholar 

  18. Savaş, E., Das, P.: A generalized statistical convergence via ideals. Appl. Math. Lett. 24, 826–830 (2011)

    Article  MathSciNet  Google Scholar 

  19. Savaş, E., Das, P., Dutta, S.: A note on strong matrix summability via ideals. Appl. Math Lett. 25(4), 733–738 (2012)

    Article  MathSciNet  Google Scholar 

  20. Savaş, E.: On \(\cal{I}\)-asymptotically lacunary statistical equivalent sequences. Adv. Differ. Equ. 2013, 2013:111 (18 April 2013)

    Google Scholar 

  21. Savaş, E.: On \(\cal{I}_{\lambda }\)-statistically convergent sequences in topological groups. Acta Comment. Univ. Tartu. Math. 18(1), 33–38 (2014)

    MathSciNet  MATH  Google Scholar 

  22. Savaş, E.: \(\Delta ^{m}\)-strongly summable sequence spaces in 2-normed spaces defined by ideal convergence and an Orlicz function. Appl. Math. Comput. 217, 271–276 (2010)

    MathSciNet  MATH  Google Scholar 

  23. Savaş, E.: A-sequence spaces in 2-normed space defined by ideal convergence and an Orlicz function. Abst. Appl. Anal. 2011 Article ID 741382 (2011)

    Google Scholar 

  24. Savaş, E.: On some new sequence spaces in 2-normed spaces using Ideal convergence and an Orlicz function. J. Ineq. Appl. Article Number 482392

    Google Scholar 

  25. Savaş, E.: On generalized double statistical convergence via ideals. In: The Fifth Saudi Science Conference 16–18 April 2012

    Google Scholar 

  26. Savaş, E.: On generalized A-difference strongly summable sequence spaces defined by ideal convergence on a real n-normed space. J. Ineq. Appl. 2012, 87 (2012)

    Article  MathSciNet  Google Scholar 

  27. Savaş, E.: On asymptotically \(\cal{I}\)-statistical equivalent sequences of order. Indian J. Math., Special Volume Dedicated to Professor Billy E. Rhoades 56(2) 1–10 (2014)

    Google Scholar 

  28. Savaş, E.: On asymptotically \(\cal{I}\)-lacunary statistical equivalent sequences of order \(\alpha \). In: The 2014 International Conference on Pure and Applied Mathematics, Venice, Italy, March 15–17 2014

    Google Scholar 

  29. Schoenberg, I.J.: The integrability of certain functions and related summability methods. Amer. Math. Monthly 66, 361–375 (1959)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Usak University, Usak, Turkey

    Ekrem Savas

  2. Department of Mathematics, Sakarya University, Sakarya, Turkey

    Rabia Savas

Authors
  1. Ekrem Savas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rabia Savas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ekrem Savas .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India

    Debdas Ghosh

  2. Department of Computer Science and Engineering, Haldia Institute of Technology, Haldia, West Bengal, India

    Debasis Giri

  3. Department of Mathematics, University of Central Florida, Orlando, FL, USA

    Ram N. Mohapatra

  4. Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan

    Kouichi Sakurai

  5. Uşak University, Uşak, Turkey

    Ekrem Savas

  6. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India

    Tanmoy Som

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Savas, E., Savas, R. (2018). An Extension Asymptotically \(\lambda \)-Statistical Equivalent Sequences via Ideals. In: Ghosh, D., Giri, D., Mohapatra, R., Sakurai, K., Savas, E., Som, T. (eds) Mathematics and Computing. ICMC 2018. Springer Proceedings in Mathematics & Statistics, vol 253. Springer, Singapore. https://doi.org/10.1007/978-981-13-2095-8_28

Download citation

Publish with us

Policies and ethics

Search

Navigation