Abstract and Applied Analysis

Starlikeness and Convexity of Generalized Struve Functions

Nihat Yagmur and Halit Orhan

Full-text: Open access

Abstract

We give sufficient conditions for the parameters of the normalized form of the generalized Struve functions to be convex and starlike in the open unit disk.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 954513, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393448862

Digital Object Identifier
doi:10.1155/2013/954513

Mathematical Reviews number (MathSciNet)
MR3035216

Zentralblatt MATH identifier
1272.30033

Citation

Yagmur, Nihat; Orhan, Halit. Starlikeness and Convexity of Generalized Struve Functions. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 954513, 6 pages. doi:10.1155/2013/954513. https://projecteuclid.org/euclid.aaa/1393448862


Export citation

References

  • A. Baricz, “Geometric properties of generalized Bessel functions,” Publicationes Mathematicae Debrecen, vol. 73, no. 1-2, pp. 155–178, 2008.
  • E. Deniz, H. Orhan, and H. M. Srivastava, “Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions,” Taiwanese Journal of Mathematics, vol. 15, no. 2, pp. 883–917, 2011.
  • E. Deniz, “Convexity of integral operators involving generalized Bessel functions,” Integral Transforms and Special Functions, vol. 1, pp. 1–16, 2012.
  • S. Owa and H. M. Srivastava, “Univalent and starlike generalized hypergeometric functions,” Canadian Journal of Mathematics, vol. 39, no. 5, pp. 1057–1077, 1987.
  • V. Selinger, “Geometric properties of normalized Bessel functions,” Pure Mathematics and Applications, vol. 6, no. 2-3, pp. 273–277, 1995.
  • H. M. Srivastava, D.-G. Yang, and N.-E. Xu, “Subordinations for multivalent analytic functions associated with the Dziok-Srivastava operator,” Integral Transforms and Special Functions, vol. 20, no. 7-8, pp. 581–606, 2009.
  • H. M. Srivastava, “Generalized hypergeometric functions and associated families of $k$-uniformly convex and $k$-starlike functions,” General Mathematics, vol. 15, no. 3, pp. 201–226, 2007.
  • H. M. Srivastava, G. Murugusundaramoorthy, and S. Sivasubramanian, “Hypergeometric functions in the parabolic starlike and uniformly convex domains,” Integral Transforms and Special Functions, vol. 18, no. 7-8, pp. 511–520, 2007.
  • D. Răducanu and H. M. Srivastava, “A new class of analytic functions defined by means of a convolution operator involving the Hurwitz-Lerch zeta function,” Integral Transforms and Special Functions, vol. 18, no. 11-12, pp. 933–943, 2007.
  • P. L. Duren, Univalent Functions, vol. 259 of Fundamental Principles of Mathematical Sciences, Springer, New York, NY, USA, 1983.
  • J. W. Alexander, “Functions which map the interior of the unit circle upon simple regions,” Annals of Mathematics, vol. 17, no. 1, pp. 12–22, 1915.
  • W. Kaplan, “Close-to-convex schlicht functions,” The Michigan Mathematical Journal, vol. 1, p. 169–185 (1953), 1952.
  • S. Ozaki, “On the theory of multivalent functions,” Science Reports of the Tokyo Bunrika Daigaku, vol. 2, pp. 167–188, 1935.
  • H. Silverman, “Univalent functions with negative coefficients,” Proceedings of the American Mathematical Society, vol. 51, pp. 109–116, 1975.
  • S. Zhang and J. Jin, Computation of Special Functions, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1996.
  • H. Orhan and N. Yağmur, “Geometric properties of generalized Struve functions,” in The International Congress in Honour of Professor Hari M. Srivastava, Bursa, Turkey, August, 2012.