On Lupaş-Jain operators

Gülen Başcanbaz-Tunca, Murat Bodur, Dilek Söylemez


In this paper, linear positive Lupaş-Jain operators are constructed and a recurrence formula for the moments is given. For the sequence of these operators; the weighted uniform approximation, also, monotonicity under convexity are obtained. Moreover, a preservation property of each Lupaş-Jain operator is presented.


Lupaş operator; Jain operator; convexity; weighted uniform approximation; modulus of continuity function

Full Text:



U. Abel, M. Ivan, On a generalization of an approximation operator de ned by A.

Lupa¸s, Gen. Math., 15 (2007), no. 1, 2134.

U. Abel, O. Agratini, Asymptotic behaviour of Jain operators, Numer Algor., 71

(2016), 553565.

O. Agratini, On a sequence of linear positive operators, Facta Univ. Ser. Math. In-

form., 14 (1999), 4148.

O. Agratini, On the rate of convergence of a positive approximation process, Nihonkai

Math., J. 11 (2000), 47-56.

O. Agratini, Approximation properties of a class of linear operators, Math. Methods

Appl. Sci., 36 (2013), no. 17, 23532358.

E.W. Cheney, A. Charma, Bernstein power series, Can. J. Math., 16 (1964), 241-252.

A. Erencin, G. Ba¸scanbaz-Tunca and F. Ta¸sdelen, Some properties of the operators

de ned by Lupa¸s, Rev. Anal. Numér. Théor. Approx., 43 (2014), no. 2, 168174.

A. Farca¸s, An asymptotic formula for Jains operators, Stud. Univ. Babe¸s-Bolyai

Math., 57 (2012), no. 4, 511517.

Z. Finta, Pointwise approximation by generalized Szász-Mirakjan operators, Stud.

Univ. Babe¸s-Bolyai Math., 46 (2001), no. 4, 6167.

Z. Finta, Quantitative estimates for some linear and positive operators, Stud. Univ.

Babe¸s-Bolyai Math., 47 (2002), no. 3, 7184.

A.D. Gadzhiev, Theorems of the type of P. P. Korovkins type theorems, Mat. Za-

metki, 20 (1976), no. 5, 781-786.

G. Gasper, M. Rahman, Basic Hypergeometric Series, Cambridge University Press,

A. Holho¸s, Quantitative estimates for positive linear operators in weighted spaces,

Gen. Math., 16 (2008), no. 4, 99110.

Z. Li, Bernstein polynomials and modulus of continuity, J. Approx. Theory, 102

(2000), no.1, 171-174.

G.C. Jain, Approximation of functions by a newclass of linear operators, J. Austral.

Math. Soc., 13 (1972), no. 3, 271276.

A. Lupa¸s, The approximation by some positive linear operators. In: Proceedings of

the International Dortmund Meeting on Approximation Theory (M.W. MÄuller et

al.,eds.), Mathematical Research, 86 (1995), 201-229, Akademie Verlag, Berlin.

H. N. Mhaskar and D. V. Pai, Fundamentals of approximation theory, CRC Press,

Boca Raton, FL; Narosa Publishing House, New Delhi, 2000.

A. Olgun, F. Ta¸sdelen and A. Erençin, A generalization of Jains operators, Appl.

Math. Comput., 266 (2015), 611.

M.A. Özarslan, Approximation Properties of Jain-Stancu Operators, Filomat, 30

(2016), no. 4, 10811088.

P. Patel, V.N. Mishra, On new class of linear and positive operators, Boll. Unione

Mat. Ital., 8 (2015), no. 2, 8196.

D.D. Stancu, M.R. Occorsio, On Approximation by binomial operators of Tiberiu

Popoviciu type, Rev. Anal. Numér. Théor. Approx., 27 (1998), 167-181.

D.J. Velleman, G.S. Call, Permutation and combination locks, Mathematics Maga-

zine, 68 (1995), no. 4, 243-253.

DOI: http://dx.doi.org/10.24193/subbmath.2018.4.08


  • There are currently no refbacks.