Surveys in Mathematics and its Applications


ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 11 (2016), 141 -- 155

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Lp- APPROXIMATION BY ITERATES OF CERTAIN SUMMATION-INTEGRAL TYPE OPERATORS

Karunesh Kumar Singh and P. N. Agrawal

Abstract. The present paper is a study of Lp- approximation in terms of higher order integral modulus of smoothness for an iterative combination due to Micchelli, of certain summation-integral type operators using the device of Steklov means.

2010 Mathematics Subject Classification: 41A30; 41A35.
Keywords: Iterative combination; Lp- approximation; modulus of smoothness; Steklov means.

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References

  1. P. N. Agrawal and K. J. Thamer, Approximation of unbounded functions by a new sequence of linear positive operators, J. Math. Anal. Appl. 225 (1998), no.~2, 660--672. MR1644320(99f:41017). Zbl 0918.41021.

  2. P. N. Agrawal and Kareem J. Thamer, On Micchelli combination of Szasz Mirakian-Durrmeyer operators. Nonlinear Funct. Anal. Appl. 13 (2008), no. 1, 135--145. MR2488418(2009j:41027). Zbl 1165.41005.

  3. V. Gupta, M.K. Gupta and V. Vasishtha, An estimate on the rate of convergence of Bézier type summation integral type operators, Kyungpook Math. J. 43 (2003), 345-354. MR2003479(2004g:41022).

  4. S. Goldberg and A. Meir, Minimum moduli of ordinary differential operators, Proc. London Math. Soc. (3) 23 (1971), 1--15. MR0300145(45 #9193). Zbl 0216.17003.

  5. E. Hewitt and K. Stromberg, Real and Abstract Analysis, McGraw-Hill, New York, 1956. MR0367121(51#3363). Zbl 0225.26001.

  6. N. Ispir and I. Yuksel, On the Bezier variant of Srivastava-Gupta operators, Appl. Math. E-Notes 5 (2005), 129--137 (electronic). MR2120140(2005i:41034). Zbl 1084.41018.

  7. C. P. May, On Phillips operator, J. Approximation Theory 20 (1977), no.~4, 315--332. MR0445177(56 #3521). Zbl 0399.41021.

  8. R. S. Phillips, An inversion formula for Laplace transforms and semi-groups of linear operators, Ann. of Math. (2) 59 (1954), 325--356. MR0060730(15,718b). Zbl 0059.10704.

  9. H. M. Srivastava and V. Gupta, A certain family of summation-integral type operators, Math. Comput. Modelling 37 (2003), no.~12-13, 1307--1315. MR1996039(2004f:41028).

  10. A. F. Timan, Theory of Approximation of Functions of Real Variables, Macmillan, New York, 1983. MR1262128(94j:41001). Zbl 0117.29001.

  11. B. Wood, p-approximation by linear combination of integral Bernstein-type operators, Anal. Numér. Théor. Approx. 13 (1984), no.~1, 65--72. MR0797800(86m:41020). Zbl 0573.41032.



Karunesh Kumar Singh
Department of Mathematics,
IIT Roorkee,
Roorkee-247667 (Uttarakhand), India.
e-mail: kksiitr.singh@gmail.com

P. N. Agrawal
Department of Mathematics,
IIT Roorkee,
Roorkee-247667 (Uttarakhand), India.
e-mail: pna_iitr@yahoo.co.in


http://www.utgjiu.ro/math/sma