Integral means and arc length of starlike log-harmonic mappings.
Integral means for certain subclasses of uniformly starlike and convex functions defined by convolution.
Integral means for starlike and convex functions with negative coefficients.
Integral means for uniformly convex and starlike functions associated with generalized hypergeometric functions.
Integral means inequalities for fractional derivatives of a unified subclass of prestarlike functions with negative coefficients.
Integral means inequalities for fractional derivatives of some general subclasses of analytic functions.
Integral means of analytic mappings by iteration of Janowski functions.
Integral means of certain analytic functions.
Integral means of certain class of analytic functions.
Integral means of certain multivalent functions.
Integral means of multivalent functions.
Integral operators of certain univalent functions.
Integral operators on a certain class of univalent functions.
Integral operators on the TUCD-class.
Integral operators which preserve the subordination.
Integral properties of certain classes of analytic functions with negative coefficients.
Integral representations of bounded starlike functions
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.
Integral transforms of functions with restricted derivatives
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....
Isomorphisms of the Disc Algebra and Iverse Faber Sets.
John disks and the pre-Schwarzian derivative.