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

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


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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© Springer India 2014

Authors and Affiliations

  1. 1.Department of MathematicsGazi UniversityTeknikokullarTurkey

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