ON CONVERGENCE PROPERTIES ASSOCIATED WITH EULER TYPE POLYNOMIALS
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The aim of this paper is to construct a generalization of Szász-type linear positive operator by using generating function method. The operator presented in the study includes the generating function of Adjoint-Euler polynomials. Many properties of this operator are explored. Moreover, the fundamental convergence properties of this operator are given. Applying this operator to the generating function of adjoint-Euler polynomials, some new formulas and relations have been derived. We also prove Voronovskaya and Grüss-Voronovskaya type theorem for this operator. Finally, some numerical results of this operator with convergence properties associated with the rate of modulus are presented.
Abstract
The aim of this paper is to construct a generalization of Szász-type linear positive operator by using generating function method. The operator presented in the study includes the generating function of Adjoint-Euler polynomials. Many properties of this operator are explored. Moreover, the fundamental convergence properties of this operator are given. Applying this operator to the generating function of adjoint-Euler polynomials, some new formulas and relations have been derived. We also prove Voronovskaya and Grüss-Voronovskaya type theorem for this operator. Finally, some numerical results of this operator with convergence properties associated with the rate of modulus are presented.
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