Direct estimate for some operators of Durrmeyer type in exponential weighted space

• Autorzy: Krech G. , Wachnicki E.
• Języki publikacji: EN

Abstrakty

EN

In the present paper, we investigate the convergence and the approximation order of some Durrmeyer type operators in exponential weighted space. Furthermore, we obtain the Voronovskaya type theorem for these operators.

Słowa kluczowe

EN

exponential weighted space; Durrmeyer type operator; convergence theorem; approximation order; Voronovskaya type theorem

PL

operator typu Durrmeyer; teoria zbieżności; aproksymacja; teoria Voronovskaya

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 2
• Strony: 336--349
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Krech G.

• Institute of Mathematics, Pedagogical University, ul. Podchorazych 2, PL-30-084 Kraków, Poland

autor

Wachnicki E.

• Institute of Mathematics, Pedagogical University, ul. Podchorazych 2, PL-30-084 Kraków, Poland

Bibliografia

• [1] O. Agratini, On a sequence of linear and positive operators, Facta Univ. Ser. Math. Inform. 14 (1999), 41–48.
• [2] J. L. Durrmeyer, Une formule d’inversion de la transformée de Laplace: Applications à la théorie des moments, Thèse de 3ème cycle, Faculté des Sciences Univ. Paris (1967).
• [3] S. M. Mazhar, V. Totik, Approximation by modified Szász operators, Acta Sci. Math. 49 (1985), 257–269.
• [4] G. M. Mirakjan, Approximation of continuous function with the aid of polynomials, Dokl. Akad. Nauk. SSSR 31 (1941), 201–205.
• [5] O. Szász, Generalization of S. Bernstein’s polynomials to the infinite interval, J. Res. Nat. Bur. Stand. Sect. B. 45 (1950), 239–245.
• [6] E. Wachnicki, On generalized Mazhar-Totik operators, Demonstratio Math. 38 (2005), 143–151.