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.
@article{bwmeta1.element.bwnjournal-article-apmv55z1p325bwm,
author = {H. M. Srivastava},
title = {Applications of certain linear operators in the theory of analytic functions},
journal = {Annales Polonici Mathematici},
volume = {55},
year = {1991},
pages = {325-330},
zbl = {0742.30013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p325bwm}
}
H. M. Srivastava. Applications of certain linear operators in the theory of analytic functions. Annales Polonici Mathematici, Tome 55 (1991) pp. 325-330. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p325bwm/
[000] [1] B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745. | Zbl 0567.30009
[001] [2] P. L. Duren, Univalent Functions, Grundlehren Math. Wiss. 259, Springer, New York 1983.
[002] [3] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms, Vol. II, McGraw-Hill, New York 1954. | Zbl 0055.36401
[003] [4] K. Nishimoto, Fractional Calculus, Vols. I, II, and III, Descartes Press, Koriyama 1984, 1987, and 1989.
[004] [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. | Zbl 0292.26011
[005] [6] S. Owa, On the distortion theorems. II, Kyungpook Math. J. 18 (1978), 53-59. | Zbl 0401.30009
[006] [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. | Zbl 0668.30013
[007] [8] S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (1987), 1057-1077. | Zbl 0611.33007
[008] [9] S. Ruscheweyh, Linear operators between classes of prestarlike functions, Comment. Math. Helv. 52 (1977), 497-509. | Zbl 0372.30007
[009] [10] M. Saigo, A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep. College General Ed. Kyushu Univ. 11 (1978), 135-145.
[010] [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). | Zbl 0617.26004
[011] [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. | Zbl 0743.30018
[012] [13] H. M. Srivastava and R. G. Buschman, Convolution Integral Equations with Special Function Kernels, Halsted Press, Wiley, New York 1977. | Zbl 0346.45010
[013] [14] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press, Wiley, New York 1984. | Zbl 0535.33001
[014] [15] H. M. Srivastava and S. Owa (eds.), Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press, Wiley, New York 1989. | Zbl 0683.00012