International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1986 / Article

Open Access

Volume 9 |Article ID 540937 | https://doi.org/10.1155/S016117128600056X

M. A. Nasr, "On alpha-close-to-convex functions of order beta", International Journal of Mathematics and Mathematical Sciences, vol. 9, Article ID 540937, 4 pages, 1986. https://doi.org/10.1155/S016117128600056X

On alpha-close-to-convex functions of order beta

Received09 Jan 1985

Abstract

Let Mβ(α)[α0andβ0] denote the class of all functionsf(z)=z+n=2anznanalytic in the unit disc U with f(z)f(z)/z0 and which satisfy for z=reiθU the condition θ1θ2Re{(1α)zf(z)f(z)+α(1+zf(z)f(z))}dθ>βπ for all θ2>θ1. In this note we show that each fMβ(α) is close-to-star of order β when 0<βα.

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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