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Modified Baskakov-Szász Operators Based on q-Integers

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Mathematical Analysis and its Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 143))

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Abstract

In the present paper we introduce the Stancu variant of certain q-modified Baskakov \(Sz\acute{a}sz\) operators. We estimate the moments of the operators and obtain some direct results in terms of the modulus of continuity. Then, we study the Voronovskaja type theorem and the rate of convergence of these operators in terms of the weighted modulus of continuity. Further, we discuss the point-wise estimation using the Lipschitz type maximal function. Finally, we investigate the rate of statistical convergence of these operators using weighted modulus of continuity.

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Acknowledgments

The authors are extremely grateful to the reviewers for careful reading of the manuscript and for making valuable suggestions leading to better presentation of the paper. The last author is thankful to the “University Grants Commission” India, for financial support to carry out the above research work.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    P. N. Agrawal & Arun Kajla

Authors
  1. P. N. Agrawal
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  2. Arun Kajla
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Corresponding author

Correspondence to Arun Kajla .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    P. N. Agrawal

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    R. N. Mohapatra

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Uaday Singh

  4. Dept. of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

    H. M. Srivastava

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Agrawal, P.N., Kajla, A. (2015). Modified Baskakov-Szász Operators Based on q-Integers. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_7

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