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Convergence Methods for Double Sequences and Applications pp 99–115Cite as

Application of Almost Convergence in Approximation Theorems for Functions of Two Variables

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Abstract

In this chapter, we apply the notion of almost convergence for double sequences to prove some Korovkin-type approximation theorems for functions of two variables through some different sets of test functions. We also give examples in support of our results, and furthermore we present some consequences of the main results.

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References

  1. G.A. Anastassiou, Approximation by Multivariate Singular Integrals (Springer, New York, 2011)

    Book  MATH  Google Scholar 

  2. G.A. Anastassiou, M. Mursaleen, S.A. Mohiuddine, Some approximation theorems for functions of two variables through almost convergence of double sequences. J. Comput. Anal. Appl. 13(1), 37–40 (2011)

    MathSciNet  MATH  Google Scholar 

  3. G. Bleimann, P.L. Butzer, L. Hahn, A Bernstein type operator approximating continuous functions on semiaxis. Indag. Math. 42, 255–262 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ö. Çakar, A.D. Gadjiev, On uniform approximation by Bleimann, Butzer and Hahn on all positive semiaxis. Trans. Acad. Sci. Azerb. Ser. Phys. Tech. Math. Sci. 19, 21–26 (1999)

    MathSciNet  MATH  Google Scholar 

  5. W. Meyer-König, K. Zeller, Bersteinsche Potenzreihen. Stud. Math. 19, 89–94 (1960)

    MATH  Google Scholar 

  6. R.N. Mohapatra, Quantitative results on almost convergence of a sequence of positive linear operators. J. Approx. Theory 20, 239–250 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  7. S.A. Mohiuddine, An application of almost convergence in approximation theorems. Appl. Math. Lett. 24, 1856–1860 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. D.D. Stancu, A method for obtaining polynomials of Bernstein type of two variables. Am. Math. Mon. 70(3), 260–264 (1963)

    Article  MathSciNet  Google Scholar 

  9. F. Taşdelen, A. Erençin, The generalization of bivariate MKZ operators by multiple generating functions. J. Math. Anal. Appl. 331, 727–735 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. V.I. Volkov, On the convergence of sequences of linear positive operators in the space of two variables. Dokl. Akad. Nauk SSSR 115, 17–19 (1957)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    M. Mursaleen

  2. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

    S. A. Mohiuddine

Authors
  1. M. Mursaleen
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  2. S. A. Mohiuddine
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Mursaleen, M., Mohiuddine, S.A. (2014). Application of Almost Convergence in Approximation Theorems for Functions of Two Variables. In: Convergence Methods for Double Sequences and Applications. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1611-7_6

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