Convex and starlike functions
Convex bodies of constant width and the Apollonian metric.
Convex combination of analytic functions
Radii of convexity, starlikeness, lemniscate starlikeness and close-to-convexity are determined for the convex combination of the identity map and a normalized convex function F given by f(z) = α z+(1−α)F(z).
Convex dynamics in Hele-Shaw cells.
Convex functions and the rolling circle criterion.
Convex functions in a half-plane.
Convex functions in a half-plane. II.
Convex hulls of polyominoes.
Convex integration and the theory of elliptic equations
This paper deals with the theory of linear elliptic partial differential equations with bounded measurable coefficients. We construct in two dimensions examples of weak and so-called very weak solutions, with critical integrability properties, both to isotropic equations and to equations in non-divergence form. These examples show that the general theory, developed in [1, 24] and [2], cannot be extended under any restriction on the essential range of the coefficients. Our constructions are based...
Convex meromorphic mappings
We study functions f(z) which are meromorphic and univalent in the unit disk with a simple pole at z = p, 0 < p < 1, and which map the unit disk onto a domain whose complement is either convex or is starlike with respect to a point w₀ ≠ 0.
Convexities of Gaussian integral means and weighted integral means for analytic functions
We first show that the Gaussian integral means of (with respect to the area measure ) is a convex function of on when . We then prove that the weighted integral means and of the mixed area and the mixed length of and , respectively, also have the property of convexity in the case of . Finally, we show with examples that the range is the best possible.
Convexity of a class of functions related to classes of starlike functions and functions with boundary rotation
Convolution and differential subordination.
Convolution and differential subordination for multivalent functions.
Convolution and Quasiconformal Extension
Convolution Conditions for Convexity, Starlikeness and Spiral-Likeness.
Convolution conditions for spirallikeness and convex spirallikeness of certain meromorphic -valent functions.
Convolution operators on spaces of holomorphic functions
A class of convolution operators on spaces of holomorphic functions related to the Hadamard multiplication theorem for power series and generalizing infinite order Euler differential operators is introduced and investigated. Emphasis is placed on questions concerning injectivity, denseness of range and surjectivity of the operators.
Convolution properties of a slanted right half-plane mapping
Convolution properties of classes of analytic and meromorphic functions.