International Journal of Mathematics Trends and Technology (IJMTT)
© 2021 by IJMTT Journal
Volume-67 Issue-2
Year of Publication : 2021
Authors : Rupesh K. Srivastav, Sheetal Deshwal


MLA Style: Rupesh K. Srivastav, Sheetal Deshwal. "CONVERGENCE: NEW POST-WIDDER OPERATORS" International Journal of Mathematics Trends and Technology 67.2 (2021):43-52. 

APA Style: Rupesh K. Srivastav, Sheetal Deshwal(2021). CONVERGENCE: NEW POST-WIDDER OPERATORS. International Journal of Mathematics Trends and Technology, 43-52.

The concern of present article is to study approximation properties of generalized form of Post-Widder operators. The modified operators conserve polynomial function αs(v) = vs, s ε N. we find some error in estimation of these operators with help of different approximation tools like usual, weighted and exponential modulus of continuity. The rate of convergence of these operators is also shown by numberical table and graphically using mathematica.


[1] T. Acar, A. Aral, I. Rasa, The new forms of Voronovskaja's theorem in weighted spaces, Positivity 20(2016), 25{40. 65(2016), 121-132.
[2] S. Deshwal, P. N. Agrawal, and A. Serkan, Modi ed Stancu operators based on inverse Polya Eggenberger distribution, J Inequal Appl. (2017.1) (2017), 1-11.
[3] S. Deshwal and P.N. Agrawal, Mihesan-Kantorovich operators of blending type, Gen. Maths. 25(1-2) (2017) 11-27.
[4] B.R. Draganov and K.G. Ivanov, A characterization of weighted approximations by the Post-Widder and the Gamma operators, J. Approx. Theory, 146 (2007), 3-27.
[5] Z. Ditzian, On global inverse theorem of Szasz and Baskakov operators, canad. J. Math. 31 (2),(1979) 255-263.
[6] V. Gupta , D. Agrawal Convergence by modi ed Post-Widder operators, RACSAM. 113(2)(2019),1475-1486.
[7] V. Gupta and R.P Agarwal, Convergence estimate in approximation theory, Springer, Cham (2014).
[8] V. Gupta and G. Tachev, Approximation with positive linear operators and linear combinations, Series developments in Mathematics, vol 50, Springer, Cham (2017).
[9] V. Gupta and G. Tachev, On approximation properties of Philips operators preserving exponential functions, Mediterr. J. Math 14(4), 177 (2017).
[10] C. P. May Saturation and inverse theorems for combinations of a class of exponential type operators Canad J Math. 28 (1976),1224-1250.
[11] L. Rempulska and M. Skorupka, On strong approximation applied to Post-Widder operators, Anal. Theory Appl., 22 (2006), 172-182.
[12] M. Sofyalioglu and K. Kanat Approximation properties of the Post-Widder operators preserving e2ax; a > 0, Math. Meth. Appl. Sci. 43(1) (2020), DOI:10.1002/mma.6192.
[13] R. A. DeVore and C. G. Lorentz, Constructive approximation, Springer, Berlin (1993).
[14] D. V. Widder, The laplace transform, Princeton mathematical series. Princeton University Press, Princeton (1941).

Keywords : Post-Widder operators, Peetre's K-functional , Exponential modulus of continuity, weighted modulus of continuity.