DOI QR코드

DOI QR Code

Subordination and Superordination for Multivalent Functions associated with the Differintegral Operator

  • Kwon, Oh Sang (Department of Mathematics, Kyungsung University) ;
  • Cho, Nak Eun (Department of Applied Mathematics, Pukyong National University)
  • Received : 2010.07.16
  • Accepted : 2012.09.14
  • Published : 2013.03.23

Abstract

The purpose of the present paper is to obtain some subordination- and superordination-preserving properties for multivalent function associated the differintegral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich type theorem for the integral operator is also considered.

Keywords

References

  1. T. Bulboaca, Integral operators that preserve the subordination, Bull. Korean Math. Soc., 32(1997), 627-636.
  2. T. Bulboaca, A class of superordination-preserving integral operators, Indag. Math. N. S., 13(2002), 301-311. https://doi.org/10.1016/S0019-3577(02)80013-1
  3. W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J., 2(1952), 169-185.
  4. S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J., 28(1981), 157-171. https://doi.org/10.1307/mmj/1029002507
  5. S. S. Miller and P. T. Mocanu, Univalent solutions of Briot-Bouquet differential equations, J. Different. Equations, 56(1985), 297-309. https://doi.org/10.1016/0022-0396(85)90082-8
  6. S. S. Miller and P. T. Mocanu, Differential subordination, Theory and Application, Marcel Dekker, Inc., New York, Basel, 2000.
  7. S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations, Complex Var. Theory Appl., 48(2003), 815-826. https://doi.org/10.1080/02781070310001599322
  8. S. S. Miller, P. T. Mocanu and M. O. Reade, Subordination-preserving integral operators, Trans. Amer. Math. Soc., 283(1984), 605-615. https://doi.org/10.1090/S0002-9947-1984-0737887-4
  9. S. Owa, On the distortion theorems I, Kyungpook Math. J., 18(1978), 53-59.
  10. S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39(1987), 1057-1077. https://doi.org/10.4153/CJM-1987-054-3
  11. S. Owa and H. M. Srivastava, Some subordination theorems involving a certain family of integral operators, Integral Transforms Spec. Funct., 15(2004), 445-454. https://doi.org/10.1080/10652460410001727563
  12. Ch. Pommerenke, Univalent Functions, Vanderhoeck and Ruprecht, Gottingen, 1975.
  13. H. M. Srivastava and M. K. Aouf, A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients. I and II , J. Math. anal. Appl., 171(1992), 1-13
  14. H. M. Srivastava and M. K. Aouf, A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients. I and II , J. Math. anal. Appl., 192(1995), 673-688. https://doi.org/10.1006/jmaa.1995.1197
  15. H. M. Srivastava and A. K. Mishra, A fractional differintegral operator and its applications to a nested class of multivalent functions with negative coefficients, Adv. Stud. Contemp. Math., 7(2003), 203-214.