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Mathematics and Computing 2013 pp 201–214Cite as

Approximation Properties of Linear Positive Operators with the Help of Biorthogonal Polynomials

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 91))

Abstract

In this paper we introduce Konhauser polynomials, Kantorovich type modification of Konhauser polynomials, and q-Laguerre polynomials. Approximation properties of these operators are obtained with the help of the Korovkin theorem. The order of convergence of these operators is computed by means of modulus continuity, Peetre’s K-functional, the elements of the Lipschitz class, and the second order modulus of smoothness. Also we introduce the r-th order generalization of these operators and we evaluate their generalizations. Finally we give some applications to differential equations for operators which include Konhauser polynomials.

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Authors and Affiliations

  1. Department of Mathematics, Gazi University, Teknikokullar, 06500, Turkey

    G. Icoz

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  1. G. Icoz
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Correspondence to G. Icoz .

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Editors and Affiliations

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

    Ram N. Mohapatra

  2. Dept of Computer Science & Engineering, Haldia Institute of Technology, Haldia, India

    Debasis Giri

  3. Ministry of Defence, Scientific Analysis Group, Defence Research and Development Organisation, New Delhi, Delhi, India

    P. K. Saxena

  4. Department of Mathematics, India Institute of Technology, Kharagpur, West Bengal, India

    P. D. Srivastava

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Icoz, G. (2014). Approximation Properties of Linear Positive Operators with the Help of Biorthogonal Polynomials. In: Mohapatra, R., Giri, D., Saxena, P., Srivastava, P. (eds) Mathematics and Computing 2013. Springer Proceedings in Mathematics & Statistics, vol 91. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1952-1_13

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