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1991 | 55 | 1 | 325-330
Tytuł artykułu

Applications of certain linear operators in the theory of analytic functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
55
Numer
1
Strony
325-330
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-09-14
Twórcy
  • Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3P4, Canada
Bibliografia
  • [1] B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745.
  • [2] P. L. Duren, Univalent Functions, Grundlehren Math. Wiss. 259, Springer, New York 1983.
  • [3] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms, Vol. II, McGraw-Hill, New York 1954.
  • [4] K. Nishimoto, Fractional Calculus, Vols. I, II, and III, Descartes Press, Koriyama 1984, 1987, and 1989.
  • [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.
  • [6] S. Owa, On the distortion theorems. II, Kyungpook Math. J. 18 (1978), 53-59.
  • [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.
  • [8] S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (1987), 1057-1077.
  • [9] S. Ruscheweyh, Linear operators between classes of prestarlike functions, Comment. Math. Helv. 52 (1977), 497-509.
  • [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] 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).
  • [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.
  • [13] H. M. Srivastava and R. G. Buschman, Convolution Integral Equations with Special Function Kernels, Halsted Press, Wiley, New York 1977.
  • [14] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press, Wiley, New York 1984.
  • [15] H. M. Srivastava and S. Owa (eds.), Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press, Wiley, New York 1989.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv55z1p325bwm
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