## Abstract

Let S denote the class of functions f(z) = z + a_{2}z^{2}+... analytic and univalent in the open unit disc D = {z ∈ C||z|<1}. Consider the subclass and S* of S, which are the classes ofconvex and starlike functions, respectively. In 1952, W. Kaplan introduced a class of analyticfunctions f(z), called close-to-convex functions, for which there existsφ(Z) ∈ C, depending on f(z) with Re( f′(z)/φ′(z) ) > 0 in , and prove that every close-to-convex function is univalent. The normalized class of close-to-convex functions denoted by K. These classesare related by the proper inclusions C ⊂ S* ⊂ K ⊂ S. In this paper, we generalize the close-to-convex functions and denote K(λ) the class of such functions. Various properties of this class of functions is alos studied.

Original language | English |
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Pages (from-to) | 2769-2775 |

Number of pages | 7 |

Journal | Applied Mathematical Sciences |

Volume | 7 |

Issue number | 53-56 |

DOIs | |

Publication status | Published - 2013 |

Externally published | Yes |

## Keywords

- Close-to-convex
- Convex
- Fractional calculus
- Starlike