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Korovkin Type Theorems for Cheney–Sharma Operators via Summability Methods

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Abstract

Korovkin type approximation theory is concerned with the convergence of the sequences of positive linear operators to the identity operator. In this paper, we deal with the Korovkin type approximation properties of the Cheney–Sharma operators by using A-statistical convergence and Abel convergence that are some well known methods of summability theory. We also study the rate of convergence. Finally, we show that the results obtained in this paper are stronger than previous ones and we support our results with particular examples and graphs.

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Authors and Affiliations

  1. Department of Computer Programming, Elmadağ Vocational School, Ankara University, 06780, Ankara, Turkey

    Dilek Söylemez

  2. Department of Mathematics, Faculty of Science, Ankara University, 06100, Tandoğan, Ankara, Turkey

    Mehmet Ünver

Authors
  1. Dilek Söylemez
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  2. Mehmet Ünver
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Correspondence to Mehmet Ünver.

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Söylemez, D., Ünver, M. Korovkin Type Theorems for Cheney–Sharma Operators via Summability Methods. Results Math 72, 1601–1612 (2017). https://doi.org/10.1007/s00025-017-0733-1

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  • DOI: https://doi.org/10.1007/s00025-017-0733-1

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