Taiwanese Journal of Mathematics

FRACTIONAL CALCULUS AND SOME PROPERTIES OF $k$-UNIFORM CONVEX FUNCTIONS WITH NEGATIVE COEFFICIENTS

H. Özlem Güney, S. Sümer Eker, and Shigeyoshi Owa

Full-text: Open access

Abstract

In this paper, we introduce a class of functions $(k,A,B,\alpha)-UCV$ which is convex in the unit disk. We give some results for the class $(k,A,B,\alpha)-UCV$, integral operators and radius of $k$-uniform convexity. Further, the proofs of distortion theorems for fractional calculus for functions $(k,A,B,\alpha)-UCV$ is given.

Article information

Source
Taiwanese J. Math., Volume 10, Number 6 (2006), 1671-1683.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404582

Digital Object Identifier
doi:10.11650/twjm/1500404582

Mathematical Reviews number (MathSciNet)
MR2275153

Zentralblatt MATH identifier
1199.30069

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 26A33: Fractional derivatives and integrals

Keywords
integral operators subordination starlike convex $k$-uniform fractional calculus

Citation

Güney, H. Özlem; Eker, S. Sümer; Owa, Shigeyoshi. FRACTIONAL CALCULUS AND SOME PROPERTIES OF $k$-UNIFORM CONVEX FUNCTIONS WITH NEGATIVE COEFFICIENTS. Taiwanese J. Math. 10 (2006), no. 6, 1671--1683. doi:10.11650/twjm/1500404582. https://projecteuclid.org/euclid.twjm/1500404582


Export citation

References

  • R. Bharati, P. Parvatham and A. Swaminathan, On subclasses of uniformly convex functions and corresponding class of starlike functions, Tamkang J. Math. 28 (1997), 17-32.
  • A. Gangadharan, T. H. Shanmugam and H. M.Srivastava, Generalized hypergeometric functions associated with $k$-uniformly convex functions, Comp. Math. Appl., 44 (2002), 1515-1526.
  • A. W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56 (1991), 87-92.
  • S. Kanas and A. Wisniowska, Conic regions and $k$-uniform convexity, J. Comp.and Math., 105 (1999)327-336.
  • S. Kanas and H. M. Srivastava, Linear operators associated with $k$-uniformly convex functions, Integral Transform. Spec. Funct., 9(2) (2000), 121-132.
  • S. Owa, On the distortion theorems, I. Kyunpook Math. J., 18 (1978), 53-59.
  • S. Owa and H. M. Srivastava, Univalent and Starlike generalized hypergeometric functions, Canad. J. Math., 39 (1987), 1057-1077.
  • H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1975), 109-116.
  • H. M. Srivastava and S. Owa, Some Characterization and distortion theorems involving fractional calculus, linear operators and certain subclasses of analytic functions, Nagoya Math. J., 106 (1987), 1-28.
  • H. M. Srivastava, M. Saigo and S. Owa, A class of distortion theorems involving certain operators of fractional calculus, J. Math. Anal. Appl., 131 (1988), 412-420.