Approximating Derivatives by a Class of Positive Linear Operators

Pandey, Bramha Dutta; Kunwar, B.

Research Article

Approximating Derivatives by a Class of Positive Linear Operators

Bramha Dutta Pandey¹*
B. Kunwar¹

Institute of Engineering and Technology, Lucknow-21 (India)

* Corresponding author

Abstract

Some Direct Theorems for the linear combinations of a new class of positive linear operators have been obtained for both, pointwise and uniform simultaneous approximations. a number of well known positive linear operators such as Gamma Operators of Muller, Post-Widder and Modified Post-Widder Operators are special cases of this class of operators.

How to Cite

B. D. Pandey, B. Kunwar, Approximating Derivatives by a Class of Positive Linear Operators, Int. J. Anal. Appl. 4 (2014), 58–67.

BibTeX

@article{Pandey2014,
  author  = {Pandey, Bramha Dutta and Kunwar, B.},
  title   = {Approximating Derivatives by a Class of Positive Linear Operators},
  journal = {Int. J. Anal. Appl.},
  volume  = {4},
  year    = {2014},
  pages   = {58--67},
  doi     = {}
}

References

[1] BRAMHA DUTTA PANDEY AND B. KUNWAR, On a class of positive linear operators(communicated).
[2] R. A. DEVORE AND G. G. LORENTZ, Constructive Approximation. Springer-Verlag Berlin Heidelberg, New York, (1993).
[3] P.P. KOROVKIN, Linear Operators and Approximation Theory (1960), Delhi. (Translated from Russian edition of 1959).
[4] B. Kunwar, Approximation of analytic functions by a class of linear positive operators, J. Approx. Theory 44. 173-182 (1985).
[5] G. G. LORENTZ, Bernstein Polynomials, Toronto (1953).
[6] C. P. MAY, Saturation and inverse theorems for combination of a class of exponential type operators. Canad. J. Math. 28,(1976), 1224-50.
[7] M. W.MULLER, Die Folge der Gamma operatoren.Thesis,Technische Hoschule,Stuttgort.(1967).
[8] Paula Anamaria Pit ¸ul, Evaluation of the approximation order by positive linear operators, Ph. D. Thesis, Universitatea Babe ¸s Bolyai(Romania) 2007.
[9] R. K. S. RATHORE, Linear combinations of linear positive operators and generating relations in special functions, Dissertation, IIT Delhi (India) (1973).
[10] R. K. S. RATHORE, Approximation of unbounded functions with Linear Positive Operators, Doctoral Dissertation, Technische Hogeschool Delft (1974).
[11] P. C. SIKKEMA AND R. K. S. RATHORE,Convolution with powers of bell shaped functions. Report, Dept. of Math. Technische Hogeschool (1976).
[12] P. C. SIKKEMA, Approximation formulae of Voronovskaya- type for certain convolution operators, J. Approx. Theory 26(1979), 26-45.
[13] A. F. TIMAN, Theory of Approximation of Functions of a Real variable, Peargamon Press (1963).