On Sakaguchi Functions

On Sakaguchi-Type Harmonic 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...

Certain Coefficient Inequalities for Sakaguchi Type Functions and Applications to Fractional Derivatives

In the present paper, sharp upper bounds of |a3 −μa2| for the functions f(z) = z + a2z + a3z + · · · belonging to a new subclass of Sakaguchi type functions are obtained. Also, application of our results for subclass of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szegö inequalities for certain classes of functions defined through fractio...

Coefficient Inequality for a Sub-class of Generalized Sakaguchi Type Functions

In this paper, we investigated the upper bounds of |a3 − μa2|, μ real, for a subclass of generalized Sakaguchi type functions of the form f(z) = z + ∑∞ n=2 anz n, in the unit disc E = {z : |z| < 1}. Results due to various authors follows as special cases. 2010 Mathematics Subject Classification. 30C50.

ACTA UNIVERSITATIS APULENSIS No 19/2009 CERTAIN COEFFICIENT INEQUALITIES FOR SAKAGUCHI TYPE FUNCTIONS AND APPLICATIONS TO FRACTIONAL DERIVATIVE OPERATOR

In the present paper, sharp upper bounds of |a3 − μa2| for the functions f(z) = z+ a2z + a3z + ... belonging to a new subclass of Sakaguchi type functions are obtained. Also, application of our results for subclass of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szegö inequalities for certain classes of functions defined through fractiona...

Differential subordination and argumental property

For analytic functions f (z) in the open unit disk E and convex functions g(z) in E, has proved one theorem which is a generalization of the result by K. Sakaguchi [K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959) 72–75]. The object of the present paper is to generalize the theorem due to Pommerenke.

Subordination Results on Subclasses Concerning Sakaguchi Functions