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Displaying 761 – 780 of 1148

On typically real functions which are generated by a fixed typically real function

Magdalena Sobczak-Kneć, Katarzyna Trąbka-Więcław (2011)

Czechoslovak Mathematical Journal

Let $T$ be the family of all typically real functions, i.e. functions that are analytic in the unit disk $Δ : = {z \in ℂ : | z | < 1}$ , normalized by $f (0) = f^{'} (0) - 1 = 0$ and such that $Im z Im f (z) \geq 0$ for $z \in Δ$ . In this paper we discuss the class $T_{g}$ defined as $T_{g} : = {\sqrt{f (z) g (z)} : f \in T}, g \in T .$ We determine the sets $⋃_{g \in T} T_{g}$ and $⋂_{g \in T} T_{g}$ . Moreover, for a fixed $g$ , we determine the superdomain of local univalence of $T_{g}$ , the radii of local univalence, of starlikeness and of univalence of $T_{g}$ .

On typical-real functions

Zbigniew Jerzy Jakubowski (1983)

Annales Polonici Mathematici

On uniformly close-to-convex functions and uniformly quasiconvex functions.

Subramanian, K.G., Sudharsan, T.V., Silverman, Herb (2003)

International Journal of Mathematics and Mathematical Sciences

On uniformly convex functions

A. W. Goodman (1991)

Annales Polonici Mathematici

We introduce a new class of normalized functions regular and univalent in the unit disk. These functions, called uniformly convex functions, are defined by a purely geometric property. We obtain a few theorems about this new class and we point out a number of open problems.

On univalence criteria.

Blezu, Dorin (2006)

General Mathematics

On univalence of an integral operator

Szymon Ignaciuk (2009)

Annales UMCS, Mathematica

We consider the problem of univalence of the integral operator [...] Imposing on functions f(z), g(z) various conditions and making use of a close-to-convexity property of the operator, we establish many suffcient conditions for univalence. Our results extend earlier ones. Some questions remain open.