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Korovkin-type approximation theorem for Bernstein operator of rough statistical convergence of triple sequences

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Abstract

We obtain a Korovkin-type approximation theorem for Bernstein polynomials of rough statistical convergence of triple sequences of positive linear operators of three variables from \(H_{\omega }\left( K\right) \) to \(C_{B}\left( K\right) ,\) where \(K=[0,\infty )\times [0,\infty )\times [0,\infty )\) and \(\omega \) is non-negative increasing function on K,  and \(C_{B}\left( K\right) \) the space of all continuous and bounded real valued functions on K.

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Authors and Affiliations

  1. Department of Mathematics, Gauhati University, Gauhati, Assam, 781014, India

    Bipan Hazarika

  2. Department of Mathematics, SASTRA University, Thanjavur, 613 401, India

    N. Subramanian

  3. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    M. Mursaleen

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  1. Bipan Hazarika
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  2. N. Subramanian
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  3. M. Mursaleen
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Correspondence to Bipan Hazarika.

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Communicated by Ferenc Weisz.

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Hazarika, B., Subramanian, N. & Mursaleen, M. Korovkin-type approximation theorem for Bernstein operator of rough statistical convergence of triple sequences. Adv. Oper. Theory 5, 324–335 (2020). https://doi.org/10.1007/s43036-019-00021-0

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  • DOI: https://doi.org/10.1007/s43036-019-00021-0

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