King-type operators related to squared Szász-Mirakyan basis

Authors

  • Adrian HOLHOȘ Technical University of Cluj-Napoca Department of Mathematics 28, Memorandumului Street 400114 Cluj-Napoca, Romania, e-mail: Adrian.Holhos@math.utcluj.ro https://orcid.org/0000-0002-9695-9157

DOI:

https://doi.org/10.24193/subbmath.2020.2.09

Keywords:

Voronovskaya formula, positive linear operators, squared Szász-Mirakyan basis, modified Bessel function, King-type operator.

Abstract

In this paper we study some approximation properties of a sequence of positive linear operators defined by means of the squared Szász-Mirakyan basis and prove that these operators behave better than the classical Szász-Mirakyan operators.

Mathematics Subject Classification (2010): 41A36, 41A60.

References

Abramowitz, M., Stegun, I.A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., New York, 1970.

Duman, O., Ozarslan, M.A., Sz´asz-Mirakjan type operators providing a better error estimation, Appl. Math. Lett., 20(2007), 1184-1188.

Favard, J., Sur les multiplicateurs d’interpolation, J. Math. Pures Appl., 23(1944), 219- 247.

Gavrea, I., Ivan, M., On a new sequence of positive linear operators related to squared Bernstein polynomials, Positivity, 23(2019), no. 3, 571-580.

Herzog, M., Approximation theorems for modified Szasz-Mirakjan operators in polynomial weight spaces, Le Mathematiche, 54(1999), 77-90.

Herzog, M., Approximation of continuous and unbounded functions, In: Selected Topics in Modern Mathematics Edition 2014, G. Gancarzewicz and M. Skrzyn´ski (eds.), Publishing House AKAPIT, Krak´ow (2014), 99-114.

Holho¸s, A., Uniform weighted approximation by positive linear operators, Stud. Univ. Babe¸s-Bolyai Math., 56(2011), no. 3, 135-146.

Holho¸s, A., Quantitative estimates of Voronovskaya type in weighted spaces, Results Math., 73:53(2018).

Holho¸s, A., Voronovskaya theorem for a sequence of positive linear operators related to squared Bernstein polynomials, Positivity, (2018), https://doi.org/10.1007/s11117-018-0625-y.

Holho¸s, A., A sequence of positive linear operators related to powered Baskakov basis, Carpathian J. Math., 35(2019), no. 1, 51-58.

Ismail, M.E.H., May, C.P., On a family of approximation operators, J. Math. Anal. Appl., 63(1978), 446-462.

King, J.P., Positive linear operators which preserve x2, Acta Math Hungar., 99(2003), no. 3, 203-208.

May, C.P., Saturation and inverse theorems for combinations of a class of exponential- type operators, Canad. J. Math., 28(1976), 1224-1250.

Mirakjan, G., Approximation des fonctions continues au moyen de polynomes de la forme e−nx ),m Ck,nxk , Dokl. Akad. Nauk, 31(1941), 201-205.

Ra¸sa, I., Entropies and Heun functions associated with positive linear operators, Appl. Math. Comput., 268(2015), 422-431.

Segura, J., Bounds for ratios of modified Bessel functions and associated Tur´an-type inequalities, J. Math. Anal. Appl., 374(2011), 516-528.

Szász, O., Generalization of S. Bernstein’s polynomials to the infinite interval, Journal of Research of the National Bureau of Standards, 45(1950), 239-245.

Yilmaz, O¨ .G., Aral, A., Ye¸sildal, F.T., On Sz´asz-Mirakyan type operators preserving polynomials, J. Numer. Anal. Approx. Theory, 46(2017), 93-106.

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Published

2020-06-05

How to Cite

HOLHOȘ, A. (2020). King-type operators related to squared Szász-Mirakyan basis. Studia Universitatis Babeș-Bolyai Mathematica, 65(2), 279–290. https://doi.org/10.24193/subbmath.2020.2.09

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