Gurhan ICOZ, Hatice ERYIGIT

Beta Generalization of Stancu-Durrmeyer Operators Involving a Generalization of Boas-Buck Type Polynomials

We deal with beta generalization of Stancu-Durrmeyer operators via a generalization of Boas-Buck type polynomials with the help of analytic functions. Approximation properties are investigated and convergence results are obtained for the operators.

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Szász, O.,“Generalization of S. Bernstein’s polynomials to the infinite interval”, Journal of Research of the National Bureau of Standarde, 45: 239–245, (1950).
Jakimovski, A., Leviatan, D.,“Generalized Szász operators for the approximation in the infinite interval”, Mathematica, 11: 97–103, (1969).
Ismail, M.E.H.,“On a generalization of Szász operators”, Mathematica, 39: 259–267, (1974).
Varma, S., Sucu, S.,İçöz, G., “Generalization of Szász operators involving Brenke type polynomials”, Computers and Mathematics with Applications, 64: 121–127, (2012).
Sucu, S., İçöz, G., Varma, S., “On some extensions of Szász operators including Boas-Buck-type polynomials”, Abstract and Applied Analysis, (2012).
İçöz, G., Varma, S., Sucu, S., “Approximation by operators including generalized Appell polynomials”, Filomat, 30: 429–440, (2016).
İçöz, G., Çekim, B., “Stancu-type generalizations of the Chan-Chyan-Srivastava operators”, Filomat, 30: 3733–3742, (2016).
Sucu, S., Varma, S., “Approximation by sequence of operators involving analytic functions”, Mathematics, 7(2): 188, (2019).
Sucu, S., Varma, S., “Generalization of Jakimovski−Leviatan type Szász operators”, Applied Mathematics and Computation, 270: 977-983, (2015).
Sucu, S., “Dunkl analogue of Szász operators”, Applied Mathematics and Computation, 244: 42- 48, (2014).
Cai, Q. B., Yüksel, İ., Dinlemez Kantar, Ü., Çekim, B., “Approximation Properties of Durrmeyer Type of-Bleimann-Butzer and Hahn Operators”, Journal of Function Spaces. Volume 2019, Article ID 7047656, 11 pages (2019).
Çekim, B., Dinlemez Kantar, Ü., Yüksel, İ., “Dunkl generalization of Szász Beta‐type operators”, Mathematical Methods in the Applied Sciences, 40 (18): 7697-7704, (2017).
Yazıcı, S., Çekim, B., “A Kantorovich type generalization of the Szász operators via two variable Hermite polynomials”, Gazi University Journal of Science, 30(4): 432-440, (2017).
Taşdelen, F., Söylemez, D., Aktaş, R., “Dunkl-Gamma type operators including Appell polynomials”, Complex Analysis and Operator Theory, 13(7): 3359-3371, (2019).
Aktaş, R., Söylemez, D., Taşdelen, F., “Stancu Type Generalization of Szász-Durrmeyer Operators Involving Brenke-Type Polynomials”, Filomat, 33(3), (2019).
Rainville, E.D., “Special Functions”, Macmillan, New York, NY, USA, (1960).
Altomare, F., Campiti, M., “Korovkin-Type Approximation Theory and Its Applications”, Appendix A by Michael Pannenberg and Appendix B by Ferdinand Beckhoff, de Gruyter Studies in Mathematics, 17; Walter de Gruyter & Co.: Berlin, Germany, (1994).
Devore, R.A., Lorentz, G.G., “Constructive Approximation”, Springer, Berlin, Germany, (1993).
Gavrea, I.,Raşa, I., “Remarks on some quantitative Korovkin-type results”, Rev.Anal. Numér. Théor. Approx., 22(2): 173–176, (1993).
Zhuk, V.V., “Functions of the Lip1 class and S. N. Bernstein’s polynomials (Russian)”, Vestnik Leningradskogo Universiteta. Matematika, Mekhanika, Astronomiya. Leningrad Univ., Leningrad., 1: 25–30, (1989).