We introduce and study two certain classes of holomorphic and bi-univalent functions associating -pseudo-starlike functions with Sakaguchi-type functions. We determine upper bounds for the Taylor–Maclaurin coefficients and for functions belonging to these classes. Further we point out certain special cases for our results.
We consider the class of sense-preserving harmonic functions defined in the unit disk and normalized so that and , where and are analytic in the unit disk. In the first part of the article we present two classes and of functions from and show that if and , then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions for parameters and are satisfied. In the second part we study the harmonic sections (partial...
For α ≥ 0 let denote the class of functions defined for |z| < 1 by integrating if α > 0, and log(1/(1-xz)) if α = 0, against a complex measure on |x| = 1. We study families of starlike functions where zf’(z)/f(z) ranges over a parabola with given focus and vertex. We prove a number of properties of these functions, among others that they are bounded and that they belong to . In general, it is only known that bounded starlike functions belong to for α > 0.
We show that functions whose derivatives lie in a half-plane are preserved under the Pommerenke, Chandra-Singh, Libera, Alexander and Bernardi integral transforms. We determine precisely how these transforms act on such functions. We prove that if the derivative of a function lies in a convex region then the derivative of its Pommerenke, Chandra-Singh, Libera, Alexander and Bernardi transforms lie in a strictly smaller convex region which can be determined. We also consider iterates of these transforms....