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Modified Stancu type Dunkl generalization of Szász–Kantorovich operators

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Abstract

In this paper, we introduce a modification of the Szász–Mirakjan–Kantorovich operators as well as Stancu operators (or a Dunkl generalization of modified Szász–Mirakjan–Kantrovich operators) which preserve the linearity. This type of modification enables better error estimation on the interval \([1/2,\infty )\) rather than the classical Dunkl Szász–Mirakjan–Kantrovich as well as Stancu operators. We obtain some approximation results via well known Korovkin’s type theorem. We also calculate the rate of convergence of operators by means of modulus of continuity and Lipschitz type maximal functions.

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Authors and Affiliations

  1. Serbian Academy of Sciences and Arts, Mathematical Institute of SASA, Kneza Mihaila 36, 11000, Belgrade, Serbia

    Gradimir V. Milovanović

  2. State University of Novi Pazar, Vuka Karadžića bb, 36300, Novi Pazar, Serbia

    Gradimir V. Milovanović

  3. Department of Mathematics, Aligarh Muslim University, 202002, Aligarh, India

    M. Mursaleen & Md. Nasiruzzaman

Authors
  1. Gradimir V. Milovanović
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  2. M. Mursaleen
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  3. Md. Nasiruzzaman
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Correspondence to Gradimir V. Milovanović.

Additional information

The work of G.V. Milovanović was supported in part by the Serbian Ministry of Education, Science and Technological Development.

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Milovanović, G.V., Mursaleen, M. & Nasiruzzaman, M. Modified Stancu type Dunkl generalization of Szász–Kantorovich operators. RACSAM 112, 135–151 (2018). https://doi.org/10.1007/s13398-016-0369-0

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  • DOI: https://doi.org/10.1007/s13398-016-0369-0

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