Advanced SearchSearch Tips
Suffciency Conditions for Hypergeometric Functions to be in a Subclasses of Analytic Functions
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 56, Issue 1,  2016, pp.235-248
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2016.56.1.235
 Title & Authors
Suffciency Conditions for Hypergeometric Functions to be in a Subclasses of Analytic Functions
Aouf, Mohamed Kamal; Mostafa, Adela Osman; Zayed, Hanaa Mousa;
  PDF(new window)
The purpose of this paper is to introduce sufficient conditions for (Gaussian) hypergeometric functions to be in various subclasses of analytic functions. Also, we investigate several mapping properties involving these subclasses.
Univalent;starlike;convex;hypergeometric functions;Hadamard product;Hohlov operator;Kim and Shon operator;
 Cited by
M. K. Aouf, A. O. Mostafa and H. M. Zayed, Necessity and suFFciency for hypergeometric functions to be in a subclass of analytic functions, J. Egyptian Math. Soc., 23(2015), 476-481. crossref(new window)

S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135(1969), 429-446. crossref(new window)

B. C. Carlson and S. B. Shaffer, Starlike and prestarlike hypergrometric functions, SIAM J. Math. Anal., 15(2002), 737-745.

P. L. Duren, Univalent Functions, Springer-Verlag, New York, 1983.

J. Dziok and H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 103(1999), 1-13. crossref(new window)

J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric functions, Integral Transforms Spec. Funct., 14(2003), 7-18. crossref(new window)

R. M. El-Ashwah, M. K. Aouf and H. M. Zayed, On certain subclass of analytic functions defined by convolution, Mat. Vesnik, 66(3)(2014), 248-264.

Yu. E. Hohlov, Operators and operations in the class of univalent functions, Izv. Vyss. Ucebn. Zaved. Matematika, 10(1978), 83-89 (in Russian).

S. Kanas and H. M. Srivastava, Linear operators associated with k-uniformly convex functions, Integral Transform. Spec. Funct., 9(2)(2000), 121-132. crossref(new window)

J. A. Kim and K. H. Shon, Mapping properties for convolutions involving hypergeo-metric functions, Internat. J. Math. Math. Sci., 17(2003), 1083-1091.

V. Kiryakova, Criteria for univalence of the Dziok-Srivastava and the Srivastava-Wright operators in the class A, Appl. Math. Comput., 218(2011), 883-892. crossref(new window)

T. H. MacGregor, The radius of convexity for starlike function of order ${\alpha}$, Proc. Amer. Math. Soc., 14(1963), 71-76.

S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Appl. Math. No. 255 Marcel Dekker, Inc., New York, 2000.

B. Pinchuk, On the starlike and convex functions of order ${\alpha}$, Duke Math. J., 35(1968), 721-734. crossref(new window)

M. S. Robertson, On the theory of univalent functions, Ann. Math. , 37(1936), 374-408. crossref(new window)

St. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49(1975), 109-115. crossref(new window)

A. Schild, On starlike function of order ${\alpha}$, Amer. J. Math., 87(1965), 65-70. crossref(new window)

N. Shukla and P. Shukla, Mapping properties of analytic function defined by hypergeometric function. II, Soochow J. Math., 25(1)(1999), 29-36.

H. M. Srivastava, Some Fox-Wright generalized hypergeometric functions and associ-ated families of convolution operators, Appl. Anal. Discrete Math., 1(2007), 56-71. crossref(new window)