Some properties of fractional calculus and linear operators associated with certain subclass of multivalent functions.

*(English)*Zbl 1177.26010Summary: We investigate several distortion inequalities involving fractional calculus, Ruscheweyh derivatives, and some well-known integral operators. In special cases, the results presented in this paper provide new approaches to several previously known results.

##### MSC:

26A33 | Fractional derivatives and integrals |

PDF
BibTeX
XML
Cite

\textit{Sh. Khosravianarab} et al., Int. J. Math. Math. Sci. 2009, Article ID 450632, 16 p. (2009; Zbl 1177.26010)

**OpenURL**

##### References:

[1] | M. K. Aouf, H. Silverman, and H. M. Srivastava, “Some families of linear operators associated with certain subclasses of multivalent functions,” Computers & Mathematics with Applications, vol. 55, no. 3, pp. 535-549, 2008. · Zbl 1155.30309 |

[2] | H. M. Srivastava, S. Owa, and O. P. Ahuja, “A new class of analytic functions associated with the Ruscheweyh derivatives,” Proceedings of the Japan Academy. Series A, vol. 64, no. 1, pp. 17-20, 1988. · Zbl 0621.30010 |

[3] | Sh. Khosravian-Arab, S. R. Kulkarni, and J. M. Jahangiri, “Certain properties of multivalent functions associated with Ruscheweyh derivative,” in Proceeding Book of the International Symposium on 2007 “Geometric Function Theory and Applications“, pp. 153-160, Istanbul Kültür University Publications, 2008. |

[4] | A. Swaminathan, “Inclusion theorems of convolution operators associated with normalized hypergeometric functions,” Journal of Computational and Applied Mathematics, vol. 197, no. 1, pp. 15-28, 2006. · Zbl 1104.30008 |

[5] | A. Swaminathan, “Certain sufficiency conditions on Gaussian hypergeometric functions,” Journal of Inequalities in Pure and Applied Mathematics, vol. 5, no. 4, article 83, pp. 1-10, 2004. · Zbl 1126.30010 |

[6] | A. Swaminathan, “Sufficiency for hypergeometric transforms to be associated with conic regions,” Mathematical and Computer Modelling, vol. 44, no. 3-4, pp. 276-286, 2006. · Zbl 1139.30308 |

[7] | R. W. Barnard, S. Naik, and S. Ponnusamy, “Univalency of weighted integral transforms of certain functions,” Journal of Computational and Applied Mathematics, vol. 193, no. 2, pp. 638-651, 2006. · Zbl 1098.30016 |

[8] | Y. C. Kim and F. Rønning, “Integral transforms of certain subclasses of analytic functions,” Journal of Mathematical Analysis and Applications, vol. 258, no. 2, pp. 466-489, 2001. · Zbl 0982.44001 |

[9] | Y. E. Hohlov, “Convolution operators preserving univalent functions,” Ukrainskiĭ Matematicheskiĭ Zhurnal, vol. 37, no. 2, pp. 220-226, 1985. · Zbl 0589.30021 |

[10] | T. Sekine, S. Owa, and K. Tsurumi, “Integral means of certain analytic functions for fractional calculus,” Applied Mathematics and Computation, vol. 187, no. 1, pp. 425-432, 2007. · Zbl 1128.30012 |

[11] | H. M. Srivastava and S. Owa, Eds., Univalent Functions, Fractional Calculus, and Their Applications, Ellis Horwood Series: Mathematics and Its Applications, Ellis Horwood, Chichester, UK; John Wiley & Sons, New York, NY, USA, 1989. · Zbl 0683.00012 |

[12] | P. K. Bernardi, “Convex and starlike univalent functions,” Transactions of the American Mathematical Society, vol. 135, pp. 429-446, 1969. · Zbl 0172.09703 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.