Pointwise Approximation By Q- Bernstein Type Operators

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-12
Year of Publication : 2020
Authors : Narendra Kumar Kurre, Feroz Khan, Mohammed Aarif Siddiqui
  10.14445/22315373/IJMTT-V66I12P504

MLA

MLA Style: Narendra Kumar Kurre, Feroz Khan, Mohammed Aarif Siddiqui "Pointwise Approximation By Q- Bernstein Type Operators" International Journal of Mathematics Trends and Technology 66.12 (2020):23-27. 

APA Style: Narendra Kumar Kurre, Feroz Khan, Mohammed Aarif Siddiqui(2020). Pointwise Approximation By Q- Bernstein Type Operators  International Journal of Mathematics Trends and Technology,23-27.

Abstract
We concern in this paper a new study of Pointwise approximation by q - Bernstein operators in the mobile interval x ∈ [−1, 1 − 1/n] with use of exponential operators and obtain the Direct theorem and Weighted approximation theorem for that operators with Rate of convergence.

Reference

[1] A.Holhas, Quantitative estimates of Voronovskaya type in weighted space, R.Math.73(2)(2018)(53).
[2] A.Holhas, A Voronovskaja Type Theorem for The first derivatives of the Positive Linear Operator, Results Math.74(2)(2019)(76).
[3] C.Jayasri, Y.Sitaramna, Direct and Inverse theorems for certain bernstein type oprators.India J.pure appl.math.16(12)(1985) 1495-1511.
[4] Gancho Tachev, Pointwise approximation by bernstein polynomials. Bull.Aust.math.soc.85(2012) 359 - 358.
[5] G. M.Phillips, Ageneralization of the Bernstein polynomials based on the q- integers,The ANZIAmM Journal 42(1)(2000)79-86.
[6] Grzegorz Nowak, Approximation properties for generalised q - Bernstein polynomials.J.math.Analysis and applications 350(1) (2009)50- 55.
[7] Heesun Jung et.al, Pointwise approximation by bernstein type operators in mobile interval.Appl.Math and comp.244(1) (2014) 683 - 694.
[8] Hubert Berens,George G.Lorentz, Inverse theorem for Bernstein polynomials,Indian univ.Math.Journal 21(8)(1972) 693-708.
[9] Kerem Kaskalaglu, Sofiya, On the q - Bernstein polynomials of piecewise linear functions in the case q >1. Math. and comp. mod. 57(9-10) (2013) 2429-2431.
[10] Narendra Kurre, Md.feroz khan,M.A.Siddiqui,Convergence of new Bernstein type operatos.IOSR, Journals of Mathematics, 16(6) (2020)37 - 43.
[11] Qing Bo Cai, Approximation properties of λ-Bernstein operators.Journals of inequalities and appl. 61(2018).
[12] S.N.Bernstein, Demantration du thereme de Weierstrass fondesur la calcul des probalities commun.soc.Math.Charkow Ser.2t. (13) (1912) 1-2.
[13] Sofiya Ostrovska, q - Bernstein polynomials and their iterates. Journal of appl. Theory 123(2003) 232- 255.
[14] V.N.Mishra, On (p; q) - Baskakov-Durmeyer-Stancu operators. Springer Inter. Publishing,27(2017)1633-1646.
[15] Z.Ditzian, Direct estimate for Bernstein polynomials. Journals of Appl. theorey 79(1994)165- 166.
[16] Zoltan Finta, Direct local and global approximation theorem for Bernstein type operators.Filomat (Nis) 18 (2004) 27- 32.

Keywords : q - Bernstein operators, Pointwise approximation, Exponential operators, Rate of convergence