Loading [MathJax]/jax/output/SVG/jax.js
\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

On modified Post-Widder operators which fix exponentials

This paper is dedicated to Professor Vijay Gupta for his 60th birthday

Abstract / Introduction Full Text(HTML) Related Papers Cited by
  • In the present work a modified Post-Widder operator is introduced which preserves a set of exponential functions. The introduction of this operator extends the class of operators which preserve exponential functions. Moments, and central moments, with some limiting properties are established. Non-weighted, and weighted, approximations are also presented. Finally, a Voronovskaya type theorem is presented.

    Mathematics Subject Classification: Primary: 41A25; Secondary: 41A30, 41A36.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] T. AcarA. AralD. Cárdenas-Morales and P. Garrancho, Szász-Mirakyan type operators which fix exponentials, Results in Mathematics, 72 (2017), 1393-1404.  doi: 10.1007/s00025-017-0665-9.
    [2] T. Acar, A. Aral and H. Gonska, On Szász-Mirakyan operators preserving e2ax, a>0, Mediterr. J. Math., 14 (2017), Paper No. 6, 14 pp. doi: 10.1007/s00009-016-0804-7.
    [3] T. AcarA. Aral and I. Raşa, Positive linear operatos preserving τ amd τ2, Constr. Math. Anal., 2 (2019), 98-102.  doi: 10.1155/2012/217464.
    [4] A. AralT. Acar and F. Ozsarac, Differentiated Bernstein type operators, Dolomites Research Notes on Approximation, 13 (2020), 47-54. 
    [5] A. AralD. Aydin Ari and B. Yilmaz, A note on Kantorovich type Bernstein-Chlodovsky operators which preserve exponential functions, Journal of Mathematical Inequalities, 15 (2021), 1173-1183.  doi: 10.7153/jmi-2021-15-78.
    [6] A. AralM. Limmam and F. Ozsarac, Approximation properties of Szász-Mirakyan-Kantorovich type operators, Math. Meth. Appl. Sci., 42 (2019), 5233-5240.  doi: 10.1002/mma.5280.
    [7] M. BodurÖ. G. Yilmaz and A. Aral, Approximation by Baskakov-Szász-Stancu operators preserving exponential functions, Constr. Math. Anal., 1 (2018), 1-8.  doi: 10.33205/cma.450708.
    [8] B. D. Boyanov and V. M. Veselinov, A note on the approximation of functions in an infinite interval by linear positive operators, Bull. Math. Soc. Sci. Math. Roum., 14 (1970), 9-13. 
    [9] E. Deniz, Quantitative estimates for Jain-Kantorovich operators, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat., 65 (2016), 121-132.  doi: 10.1501/Commua1_0000000764.
    [10] Z. Finta and V. Gupta, Direct and inverse estimates for Phillips type operators, J. Math. Anal. Appl., 303 (2005), 627-642.  doi: 10.1016/j.jmaa.2004.08.064.
    [11] A. D. Gadzhiev, The convergence problem for a sequence of positive linear operators on unbounded sets, and theorems analogous to that of P. P. Korovkin, Sov. Math. Dokl., 15 (1974), 1433-1436. 
    [12] A. D. Gadzhiev, Theorems of the type of P. P. Korovkin type theorems, Mathematical Notes of the Academy of Sciences of the USSR, 20 (1976), 995-998.  doi: 10.1007/BF01146928.
    [13] V. Gupta and A. Aral, A note on Szász-Mirakyan-Kantorovich type operators preserving ex, Positivity, 22 (2018), 415-423.  doi: 10.1007/s11117-017-0518-5.
    [14] V. Gupta, A. Aral and F. Ozsarac, On semi-exponential Gauss-Weierstrass operators, Analysis and Mathematical Physics, 12 (2022), 1-16. doi: 10.1007/s13324-022-00723-4.
    [15] V. Gupta and G. Tachev, On approximation properties of Phillips operators preserving exponential functions, Mediterranean Journal of Mathematics, 14 (2017), Paper No. 177, 12 pp. doi: 10.1007/s00009-017-0981-z.
    [16] A. Holhoş, The rate of approximation of functions in an infinite interval by positive linear operators, Stud. Univ. Babeş-Bolyai Math., 2 (2010), 133-142. 
    [17] C. P. May, Saturation and inverse theorems for combinations of a class of exponential-type operators, Canad. J. Math., 28 (1976), 1224-1250.  doi: 10.4153/CJM-1976-123-8.
    [18] F. Ozsarac and T. Acar, Reconstruction of Baskakov operators preserving some exponential functions, Math. Meth. Appl. Sci., 42 (2019), 5124-5132.  doi: 10.1002/mma.5228.
    [19] F. OzsaracV. Gupta and A. Aral, Approximation by some Baskakov-Kantorovich exponential-type operators, Bulletin of the Iranian Mathematical Society, 48 (2022), 227-241.  doi: 10.1007/s41980-020-00513-3.
    [20] L. Rempulska and M. Skorupka, On approximation by post-Widder and Stancu operators preserving x2, Kyungpook Math. J., 49 (2009), 57-65.  doi: 10.5666/KMJ.2009.49.1.057.
    [21] G. Uysal, On a special class of modified integral operators preserving some exponential functions, Mathematical Foundations of Computing, 6 (2023), 78-93. 
    [22] D. V. WidderThe Laplace Transform, Princeton Mathematical Series, Princeton University Press, Princeton, N.J., 1941. 
    [23] B. YilmazG. Uysal and and A. Aral, Reconstruction of two approximation processes in order to reproduce eax and e2ax; a>0, Journal of Mathematical Inequalities, 15 (2021), 1101-1118.  doi: 10.7153/jmi-2021-15-75.
  • 加载中
SHARE

Article Metrics

HTML views(2102) PDF downloads(91) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return