Nasze serwisy używają informacji zapisanych w plikach cookies. Korzystając z serwisu wyrażasz zgodę na używanie plików cookies zgodnie z aktualnymi ustawieniami przeglądarki, które możesz zmienić w dowolnej chwili. Więcej informacji odnośnie plików cookies.

Obowiązek informacyjny wynikający z Ustawy z dnia 16 listopada 2012 r. o zmianie ustawy – Prawo telekomunikacyjne oraz niektórych innych ustaw.

Wyłącz komunikat

 
 

Logowanie

Logowanie za pomocą Centralnej Usługi Uwierzytelniania PRz. Po zakończeniu pracy nie zapomnij zamknąć przeglądarki.

Journal of Mathematics and Applications

Journal of Mathematics and Applications
9/40, DOI: 10.7862/rf.2017.9

Approximation by Szász Type Operators Including Sheffer Polynomials

N. Rao, A. Wafi, Deepmala

DOI: 10.7862/rf.2017.9

Abstract

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.

Full text (pdf)

References

[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 convergence 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.

 

About this Article

TITLE:
Approximation by Szász Type Operators Including Sheffer Polynomials

AUTHORS:
N. Rao (1)
A. Wafi (2)
Deepmala (3)

AUTHORS AFFILIATIONS:
(1) Department of Mathematics, Jamia Mllia Islamia, New Delhi, India 
(2) Department ofMathematics, Jamia Millia Islamia, New Delhi, India
(3) Indian Institute of Information Technology Design and Manufacturing, Jabalpur, India

JOURNAL:
Journal of Mathematics and Applications
9/40

KEY WORDS AND PHRASES:
Szász operators; Sheffer Polynomials; Voronovskaya

FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/58

DOI:
10.7862/rf.2017.9

URL:
http://dx.doi.org/10.7862/rf.2017.9

RECEIVED:
2016-11-30

COPYRIGHT:
Oficyna Wydawnicza Politechniki Rzeszowskiej, al. Powstańców Warszawy 12, 35-959 Rzeszów

POLITECHNIKA RZESZOWSKA im. Ignacego Łukasiewicza; al. Powstańców Warszawy 12, 35-959 Rzeszów
tel.: +48 17 865 11 00, fax.: +48 17 854 12 60
Administrator serwisu: