On uniformly convex functions
- A. Goodman
- Mathematics
- 1991
We introduce a new class of normalized functions regular and univalent in the unit disk. These functions, called uniformly convex functions, are dened by a purely geometric property. We obtain a few…
UNIVALENT FUNCTIONS AND NONANALYTIC CURVES
- A. Goodman
- Mathematics
- 1 March 1957
The two examples z+ (1 +e)z2/2 and z+(1 +e)z2/4 with e>0, show that the right sides of (2) and (3) cannot be increased without destroying respectively the starlikeness and convexity of the image…
On uniformly starlike functions
- A. Goodman
- Mathematics
- 1 March 1991
On Sets of Acquaintances and Strangers at any Party
- A. Goodman
- Mathematics
- 1 November 1959
(1959). On Sets of Acquaintances and Strangers at any Party. The American Mathematical Monthly: Vol. 66, No. 9, pp. 778-783.
The Representation of a Graph by Set Intersections
- P. Erdös, A. Goodman, L. Pósa
- MathematicsCanadian Journal of Mathematics - Journal…
- 1966
Geometrically, a graph is a collection of points (or vertices) together with a set of edges (or curves) each of which joins two distinct vertices of the graph, and no two of which have points in…
On univalent functions convex in one direction
- A. Goodman, E. Saff
- Mathematics
- 1 February 1979
Let f(z) = z + "L2akzk be analytic and univalent in the unit disk E: \z\ < 1 and map the disk onto a domain which is convex in the direction of the imaginary axis. We show by example that for V2 -1 <…
On the Schwarz-Christoffel transformation and $p$-valent functions
- A. Goodman
- Mathematics
- 1 February 1950
maps the open unit circle |z I < 1 (hereafter denoted by E) onto P the interior of an m-sided convex polygon. The vertices of the polygon are wj =fi(%) and the exterior angle(2) at the vertex wj is…
On some determinants related to -valent functions
- A. Goodman
- Mathematics
- 1948
is univalent in E, then |ft„| ^«|fti|. This conjecture has been proved in many special cases and has a long history (3). To the best of our knowledge it has not been generalized to the class of…
A Circle Covering Theorem
- A. Goodman, R. Goodman
- Mathematics
- 1 November 1945
THEOREM 1. Let the circles C1, , C,, with radii ri, * , r,, lie in a plane and have the following property: No line of the plane divides the circles into two non-empty sets without touching or…
FUNCTIONS TYPICALLY-REAL AND MEROMORPHIC IN THE UNIT CIRCLE
- A. Goodman
- Philosophy, Mathematics
- 1956
This concept has been extended in several directions in [4; 6; 10; 11; 13; 161]. In the present paper we initiate the study of functions which are meromorphic in E but still satisfy the condition…
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