Approximation with modified Phillips operators

Volume 10, Issue 11, pp 5803--5812 http://dx.doi.org/10.22436/jnsa.010.11.18

Publication Date: November 17, 2017 Submission Date: May 31, 2017

Download PDF

Download XML

1829 Downloads
3646 Views

Authors

Danyal Soybaş - Department of Mathematics Education, Faculty of Education, Erciyes University, Kayseri 38039, Turkey.

Abstract

In the present paper, we study modified Phillips operators in simultaneous approximation. The operators discussed here are important as they have link with the well-known Szász operators. We estimate some direct results for the operators.

Share and Cite

ISRP Style

Danyal Soybaş, Approximation with modified Phillips operators, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 5803--5812

AMA Style

Soybaş Danyal, Approximation with modified Phillips operators. J. Nonlinear Sci. Appl. (2017); 10(11):5803--5812

Chicago/Turabian Style

Soybaş, Danyal. "Approximation with modified Phillips operators." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 5803--5812

Keywords

Szász operators
Phillips operators
simultaneous approximation
modulus of continuity
moment generating function
asymptotic formula
error estimation

MSC

41A25
41A30

References

[1] Z. Finta, V. Gupta, Direct and inverse estimates for Phillips type operators, J. Math. Anal. Appl., 303 (2005), 627–642.

[2] S. G. Gal, V. Gupta, Complex form of a link operator between the Phillips and the Szász-Mirakjan operators, Results Math., 67 (2015), 381–393.

[3] S. Goldberg, A. Meir, Minimum moduli of ordinary differential operators, Proc. London Math. Soc., 23 (1971), 1–15.

[4] N. K. Govil, V. Gupta, M. A. Noor, Simultaneous approximation for the Phillips operators , Int. J. Math Math. Sci., 2006 (2006), 9 pages.

[5] V. Gupta, A note on modified Phillips operators, Southeast Asian Bull. Math., 34 (2010), 847–851.
- MathSciNet
- MATH

[6] V. Gupta, On Approximation Properties of Szász-Mirakyan Operators, Springer Optim. Appl., New York (2014)

[7] V. Gupta, R. P. Agarwal, Convergence Estimates in Approximation Theory, Springer, New York (2014)
- View Article
- MathSciNet

[8] V. Gupta, G. S. Srivastava , On the rate of convergence of Phillips operators for functions of bounded variation, Comment. Math., 36 (1996), 123–130.
- MathSciNet
- Google Scholar

[9] V. Gupta, G. Tachev, On approximation properties of Phillips operators preserving exponential functions, Mediterr. J. Math., 2017 (2017), 12 pages.

[10] M. Heilmann, G. Tachev, Commutativity, direct and strong converse results for Phillips operators , East J. Approx., 17 (2011), 299–317.

[11] E. Hewitt, K. Stromberg , Real and abstract Analysis, Springer-Verlag, New York (1956)
- Google Scholar

[12] S. M. Mazhar, V. Totik, Approximation by modified Szasz operators, Acta Sci. Math., 49 (1985), 257–269.
- Google Scholar

[13] R. Păltănea, Modified Szász-Mirakjan operators of integral form, Carpathian J. Math., 24 (2008), 378–385.
- Google Scholar
- MATH

[14] R. Păltănea, Simultaneous approximation by a class of Szász Mirakjan operators, J. Appl. Funct. Anal., 9 (2014), 356–368.

[15] R. S. Phillips, An inversion formula for Laplace transforms and semi-groups of linear operators, Ann. of Math., 59 (1954), 325–356.

[16] O. Szasz, Generalization of S. Bernstein’s polynomials to the infinite interval, J. Research Nat. Bur. Standards, 45 (1950), 239–245.
- MathSciNet
- Google Scholar

[17] G. Tachev, Approximation of bounded continuous functions by linear combinations of Phillips operators, Demonstr. Math., 47 (2014), 662–671.