Results in Mathematics

, Volume 70, Issue 3–4, pp 433–446 | Cite as

Some Weighted Equi-Statistical Convergence and Korovkin Type-Theorem

  • Naim L. BrahaEmail author


In this paper, we will show a new weighted equi-statistical convergence and based on this definition we will prove a kind of the Korovkin type theorems. Also we will show the rate of the convergence for this kind of weighted statistical convergence and Voronovskaya type theorem.


Weighted equi-statistical convergence Korovkin type theorem rate of convergence Voronovskaya type theorem 

Mathematics Subject Classification

40A05 40G15 41A36 


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  1. 1.
    Altomare F.: Korovkin-type theorems and approximation by positive linear operators. Survey Approx. Theory 5, 92–164 (2010)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Balcerzak M., Dems K., Komisarski A.: Statistical convergence and ideal convergence for sequences of functions. J. Math. Anal. Appl. 328, 715–729 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Braha N.L., Loku V., Srivastava H.M.: \({\Lambda^2}\)-weighted statistical convergence and Korovkin and Voronovskaya type theorems. Appl. Math. Comput. 266, 675–686 (2015)MathSciNetGoogle Scholar
  4. 4.
    Braha N.L., Srivastava H.M., Mohiuddine S.A.: A Korovkin’s type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean. Appl. Math. Comput. 228, 162–169 (2014)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Edely O.H.H., Mohiuddine S.A., Noman A.K.: Korovkin type approximation theorems obtained through generalized statistical convergence. Appl. Math. Lett. 23, 1382–1387 (2010)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Fast H.: Sur la convergence statistique. Colloq. Math. 2, 241–244 (1951)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Karakus S., Demirci K., Duman O.: Equi-statistical convergence of positive linear operators. J. Math. Anal. Appl. 339(2), 1065–1072 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Korovkin, P.P.: Convergence of linear positive operators in the spaces of continuous functions (Russian). Doklady Akad. Nauk. SSSR (N.S.) 90, 961–964 (1953)Google Scholar
  9. 9.
    Korovkin, P.P.: Linear Operators and Approximation Theory. Hindustan Publ. Co., Delhi (1960)Google Scholar
  10. 10.
    Loku, V., Braha N.L.: \({\Lambda^2}\)− statistical convergence and its applications to Korovkin second type theorem. Thai J. Math. (2016, to appear)Google Scholar
  11. 11.
    Moricz F., Orhan C.: Tauberian conditions under which statistical convergence follows from statistical summability by weighted means. Studia Sci. Math. Hung. 41(4), 391–403 (2004)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Mursaleen M., Alotaibi A.: Statistical lacunary summability and a Korovkin type approximation theorem. Ann. Univ. Ferrara 57(2), 373–381 (2011)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Mursaleen M., Karakaya V., Erturk M., Gursoy F.: Weighted statistical convergence and its application to Korovkin type approximation theorem. Appl. Math. Comput. 218, 9132–9137 (2012)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Srivastava H.M., Mursaleen M., Khan A.: Generalized equi-statistical convergence of positive linear operators and associated approximation theorems. Math. Comput. Model. 55, 2040–2051 (2012)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Steinhaus H.: Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. 2, 73–74 (1951)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Computer SciencesUniversity of PrishtinaPrishtineKosova

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