Applications of certain linear operators in the theory of analytic functions

H. M. Srivastava

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 325-330
  • ISSN: 0066-2216

Abstract

top
The object of the present paper is to illustrate the usefulness, in the theory of analytic functions, of various linear operators which are defined in terms of (for example) fractional derivatives and fractional integrals, Hadamard product or convolution, and so on.

How to cite

top

H. M. Srivastava. "Applications of certain linear operators in the theory of analytic functions." Annales Polonici Mathematici 55.1 (1991): 325-330. <http://eudml.org/doc/262248>.

@article{H1991,
abstract = {The object of the present paper is to illustrate the usefulness, in the theory of analytic functions, of various linear operators which are defined in terms of (for example) fractional derivatives and fractional integrals, Hadamard product or convolution, and so on.},
author = {H. M. Srivastava},
journal = {Annales Polonici Mathematici},
language = {eng},
number = {1},
pages = {325-330},
title = {Applications of certain linear operators in the theory of analytic functions},
url = {http://eudml.org/doc/262248},
volume = {55},
year = {1991},
}

TY - JOUR
AU - H. M. Srivastava
TI - Applications of certain linear operators in the theory of analytic functions
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 325
EP - 330
AB - The object of the present paper is to illustrate the usefulness, in the theory of analytic functions, of various linear operators which are defined in terms of (for example) fractional derivatives and fractional integrals, Hadamard product or convolution, and so on.
LA - eng
UR - http://eudml.org/doc/262248
ER -

References

top
  1. [1] B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745. Zbl0567.30009
  2. [2] P. L. Duren, Univalent Functions, Grundlehren Math. Wiss. 259, Springer, New York 1983. 
  3. [3] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms, Vol. II, McGraw-Hill, New York 1954. Zbl0055.36401
  4. [4] K. Nishimoto, Fractional Calculus, Vols. I, II, and III, Descartes Press, Koriyama 1984, 1987, and 1989. 
  5. [5] K. B. Oldham and J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press, New York-London 1974. Zbl0292.26011
  6. [6] S. Owa, On the distortion theorems. II, Kyungpook Math. J. 18 (1978), 53-59. Zbl0401.30009
  7. [7] S. Owa, M. Saigo, and H. M. Srivastava, Some characterization theorems for starlike and convex functions involving a certain fractional integral operator, J. Math. Anal. Appl. 140 (1989), 419-426. Zbl0668.30013
  8. [8] S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (1987), 1057-1077. Zbl0611.33007
  9. [9] S. Ruscheweyh, Linear operators between classes of prestarlike functions, Comment. Math. Helv. 52 (1977), 497-509. Zbl0372.30007
  10. [10] M. Saigo, A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep. College General Ed. Kyushu Univ. 11 (1978), 135-145. 
  11. [11] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order and Some of Their Applications, Nauka i Tekhnika, Minsk 1987 (in Russian). Zbl0617.26004
  12. [12] N. S. Sohi, Distortion theorems involving certain operators of fractional calculus on a class of p-valent functions, in: Fractional Calculus and Its Applications, K. Nishimoto (ed.), College of Engineering (Nihon University), Koriyama 1990, 245-252. Zbl0743.30018
  13. [13] H. M. Srivastava and R. G. Buschman, Convolution Integral Equations with Special Function Kernels, Halsted Press, Wiley, New York 1977. Zbl0346.45010
  14. [14] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press, Wiley, New York 1984. Zbl0535.33001
  15. [15] H. M. Srivastava and S. Owa (eds.), Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press, Wiley, New York 1989. Zbl0683.00012

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.