A recent result of Yalcin [9] appeared in Applied Mathematics Letters (2005), concerning the convolution of two harmonic univalent functions in class SH(m,n, α) is improved. AMS (MOS) Subject Classification Codes: 30C45

In the present paper, we consider a generalised subclass of analytic functions involving arithmetic, geometric and harmonic means. For this function class we obtain an inclusion result, Fekete-Szegö inequality and coefficient bounds for bi-univalent functions.

We consider the Sakaguchi functions which are starlike with respect to symmetrical points in the open unit disk U and extend it to class SH(α, t) concerning with Sakaguchi-type complex-valued harmonic univalent functions in U. A sufficient coefficient condition and a necessary and sufficient convolution characterization for such harmonic functions are determined. In addition, by using the coeff...

Inequalities involving multipliers using the sequences {cn} and {dn} of positive real numbers are introduced for complex-valued harmonic univalent functions. By specializing {cn} and {dn}, we determine representation theorems, distortion bounds, convolutions, convex combinations, and neighbourhoods for such functions. The theorems presented, in many cases, confirm or generalize various well-kno...