Approximation by Szász type operators including Sheffer polynomials

• Autorzy: Rao N. , Wafi A. , Deepmala A.

Identyfikatory

DOI

10.7862/rf.2017.9

• Języki publikacji: EN

Abstrakty

EN

In present article, we discuss voronowskaya type theorem, weighted approximation in terms of weighted modulus of continuity for Szász type operators using Sheffer polynomials. Lastly, we investigate statistical approximation for these sequences.

Słowa kluczowe

EN

Szász operators; Sheffer polynomials; Voronovskaya type theorem

PL

operatory Szásza; wielomiany Sheffera; twierdzenie typu Woronowskiej

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2017
• Tom: Vol. 40
• Strony: 135--148
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Rao N.

• Department of Mathematics, Jamia Millia Islamia, New Delhi - 110025, India

autor

Wafi A.

• Department of Mathematics, Jamia Millia Islamia, New Delhi - 110025, India

autor

Deepmala A.

• Mathematics Discipline, PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur - 482005, India

Bibliografia

• [1] S.N. Bernstein, Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités, Comm. Soc. Math. Kharkow 2 13 (1912) 1-2.
• [2] P.L. Butzer, R.J. Nessel, Fourier Analysis and Approximation, Birkhäuser, Bessel and Academic Press, New York 1 1971.
• [3] M.E.H. Ismail, On a generalization of Szász operators, Mathematica (Cluj) 39 (1974) 259-267.
• [4] A. Jakimovski, D. Leviatan, Generalized Szász operators for the approximation in the infinite interval, Mathematica (Cluj) 11 (1969) 97-103
• [5] L. Rempulska, M. Skorupka, The Voronovskaya theorem for some operators of the Szász-Mirakjan type, Le Matematiche 2 50 (1995) 251-261
• [6] O. Szász, Generalization of S. Bernstein’s polynomials to the infinite interval, J. Research Nat. Bur. Standards 45 (1950) 239-245.
• [7] S. Sucu, E. Ibikli, Rate of convergance of Szász type operators including Sheffer polynomials, Stud. Univ. Babes-Bolyai Math. 1 58 (2013) 55-63.
• [8] E. Voronovskaja, Détermination de la forme asymptotique de L'approximation des functions par les polynômes de M. Bernstein, C. R. Acad. Sci. URSS 1932 (1932) 79-85.
• [9] A.R. Gairola, Deepmala and L.N. Mishra, Rate of approximation by finite iterates of q-Durrmeyer operators, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 86 2 (2016) 229-234.
• [10] K.K. Singh, A.R. Gairola and Deepmala, Approximation theorems for q-analouge of a linear positive operator by A. Lupas, Int. J. Anal. Appl. 12 1 (2016) 30-37.
• [11] A.D. Gadjiev, Theorems of the type of P.P. Korovkin’s theorems, Math. Zametki 20 5 (1976) 781-786 (in Russian), Math. 20 5-6 (1976) 995-998 (in English).
• [12] E. Ibikli, E.A. Gadjieva, The order of approximation of some unbounded functions by the sequence of positive linear operators, Turkish J. Math. 19 3 (1995) 331-337.
• [13] I. Yüksel, N. Ispir, Weighted approximation by a certain family of summation integral-type operators, Comput. Math. Appl. 52 10-11 (2006) 1463-1470.
• [14] A.D. Gadjiev, C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 1 (2007) 129-138.
• [15] O. Duman, C. Orhan, Statistical approximation by positive linear operators, Studia Math. 16 2 (2004) 187-197.
• [16] V.N. Mishra, K. Khatri, L.N. Mishra and Deepmala, Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators, Journal of Inequalities and Applications (2013) 2013:586, doi:10.1186/1029-242X-2013-586.
• [17] V.N. Mishra, H.H. Khan, K. Khatri and L.N. Mishra, Hypergeometric representation for Baskakov-Durrmeyer-Stancu type operators, Bulletin of Mathematical Analysis and Applications 5 3 (2013) 18-26.
• [18] V.N. Mishra, K. Khatri and L.N. Mishra, On simultaneous approximation for Baskakov-Durrmeyer-Stancu type operators, Journal of Ultra Scientist of Physical Sciences 24 3 A (2012) 567-577.
• [19] V.N. Mishra, K. Khatri and L.N. Mishra, Some approximation properties of q-Baskakov-Beta-Stancu type operators, Journal of Calculus of Variations, Volume 2013 (2013) Article ID 814824, 8 pages, http://dx.doi.org/10.1155/2013/814824.
• [20] V.N. Mishra, K. Khatri and L.N. Mishra, Statistical approximation by Kantorovich type discrete q-beta operators, Advances in Difference Equations (2013) 2013:345, doi: 10.1186/10.1186/1687-1847-2013-345.
• [21] V.N. Mishra, P. Sharma and L.N. Mishra, On statistical approximation properties of q-Baskakov-Szász-Stancu operators, Journal of Egyptian Mathematical Society 24 3 (2016) 396-401, doi: 10.1016/j.joems.2015.07.005.
• [22] R.B. Gandhi, Deepmala and V.N. Mishra, Local and global results for modified Szász-Mirakjan operators, Math. Method. Appl. Sci. (2016), doi: 10.1002/mma.4171.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).