A convolution approach on partial sums of certain analytic and univalent functions. (English) Zbl 1226.30013

Dixit, K. K.; Porwal, Saurabh

JIPAM, J. Inequal. Pure Appl. Math. 10, No. 4, Paper No. 101, 9 p. (2009).

Summary: We determine sharp lower bounds for \(\mathrm{Re}\left\{\frac{f(z)\ast \psi(z)}{f_{n}(z)\ast \psi(z)} \right\}\) and \(\mathrm{Re}\left\{\frac{f_n(z)\ast\psi(z)}{f(z)\ast\psi(z)}\right\}\). We extend some known results and correct certain conditions in theorems by B. A. Frasin, T. Rosy, K. G. Subramanian and G. Murugusundaramoorthy, as well as R. K. Raina and D. Bansal.

MSC:

30C45

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

analytic functions; univalent functions; convolution; partial sums