A Note on the Differences of Two Positive Linear Operators

Year 2019, Volume: 2 Issue: 1, 1 - 7, 01.03.2019

Gancho Tachev Vijay Gupta

https://doi.org/10.33205/cma.469114

Cited By: 6

Abstract

In the present note we find the general estimate in terms of Paltanea's modulus of continuity. In the end, we consider some examples and we apply our result for such examples to obtain the quantitative estimates for the difference of operators.

Keywords

Weighted modulus, Baskakov operators, Phillips operators, Difference of operators, Szasz-Mirakyan operators, Lupaş operators, Difference of operators

References

• [1] T. Acar, A. Aral and I. Raşa: The new forms of Voronovskaja’s theorem in weighted spaces, Positivity 20 (2016), 25-40.
• [2] A. M. Acu and I. Raşa: New estimates for differences of positive linear operators, Numer. Algor. 73 (2016), 775-789.
• [3] A. Aral, D. Inoan and I. Raşa: On differences of linear positive operators, Anal. Math. Phys. doi 13324-018-0227-7.
• [4] H. Gonska, P. Pitul and I. Raşa: On differences of positive linear operators, Carpathian J. Math. 22(1-2) (2006), 65-78.
• [5] H. Gonska, and I. Raşa: Differences of positive linear operators and the second order modulus, Carpathian J. Math. 24(3) (2008), 332-340.
• [6] V. Gupta: Differences of operators of Lupaş type, Constructive Mathematical Analysis 1(1) (2018), 9-14.
• [7] V. Gupta, T. M. Rassias, P. N. Agrawal and A. M. Acu: Recent Advances in Constructive Approximation Theory, Springer, Cham. (2018).
• [8] V. Gupta and G. Tachev: General form of Voronovskaja’s theorem in terms of weighted modulus of continuity, Results Math 69 (3-4) (2016), 419-430.
• [9] V. Gupta and G. Tachev: Approximation with Positive Linear Operators and Linear Combinations, Springer, Cham. 2017.
• [10] R. Paltanea: Estimates of approximation in terms of a weighted modulus of continuity, Bull. Transilvania Univ. of Brasov 4 (53) (2011), 67-74.