The punishing factors for convex pairs are .
The quasi-Hadamard products of uniformly convex functions defined by Dziok-Srivastava operator
The quasihyperbolic metric, growth, and John domains.
The radius of close-to-convexity of
The radius of conformity of some classes of regular functions
The radius of convexity of certain analytic functions. II.
The radius of starlikeness for convex functions of complex order.
The radius of starlikeness of the certain classes of -valent functions defined by multiplier transformations.
The radius of univalence and starlikeness of a certain class of analytic functions
The radius of univalence and starlikeness of some classes of regular functions
The radius of univalence of certain analytic functions
The Riemannian structure of John and uniform domains in .
The Riesz kernels do not give rise to higher dimensional analogues of the Menger-Melnikov curvature.
Ever since the discovery of the connection between the Menger-Melnikov curvature and the Cauchy kernel in the L2 norm, and its impressive utility in the analytic capacity problem, higher dimensional analogues have been coveted. The lesson from 1-sets was that any such (nontrivial, nonnegative) expression, using the Riesz kernels for m-sets in Rn, even in any Lk norm (k ∈ N), would probably carry nontrivial information on whether the boundedness of these kernels in the appropriate norm implies rectifiability...
The roots of a polynomial depend continuously on its coefficients.
The Schwarz-Christoffel conformal mapping for “polygons” with infinitely many sides.
The Schwarz-Christoffel conformal mapping for "polygons" with infinitely many sides.
The Schwarzian derivative and conformally natural quasiconformal extensions from one to two to three dimensions.
The Schwarzian derivative for conformal maps.
The Schwarz-Pick theorem and its applications
Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmén-Lindelöf principle, which is of course standard in such situations.
The second coefficient of a function with all derivatives univalent.