Uniformly convex functions and a corresponding class of starlike functions
- F. Rønning
- Mathematics
- 1993
We investigate starlike functions f(z) = z + Yfk=2akzk wim the property that zf'(z)/'f(z) lies inside a certain parabola. These functions are closely related to a class of functions called uniformly…
Integral Transforms of Certain Subclasses of Analytic Functions
- Yong Chan Kim, F. Rønning
- Mathematics
- 15 June 2001
Abstract Let A be the class of normalized analytic functions in the unit disk Δ and define the class P γ β = f ∈ A | ∃ϕ ∈ R | Re e i ϕ 1 − γ f z / z + γ f ′ z − β > 0, z ∈ Δ . For a function f ∈ A…
Integral representations of bounded starlike functions
- F. Rønning
- Mathematics
- 1995
For α ≥ 0 let Fα denote the class of functions defined for |z| < 1 by integrating 1/(1− xz) if α > 0, and log(1/(1− xz)) if α = 0, against a complex measure on |x|=1. We study families of starlike…
Integral transforms of a class of analytic functions
- S. Ponnusamy, F. Rønning
- Mathematics
- 15 April 2008
For γ ≥ 0 and β < 1 given, let 𝒫γ(β) denote the class of all analytic functions f in the unit disc with the normalization f(0) = f ′(0) − 1 = 0 and satisfying the condition for some φ ∈ ℝ. The main…
Influence of computer-aided assessment on ways of working with mathematics
- F. Rønning
- Computer Science
- 1 June 2017
On a multiplier conjecture for univalent functions
- V. Gruenberg, F. Rønning, S. Ruscheweyh
- Mathematics
- 1990
Let Y be the set of normalized univalent functions, and let 0 be the subset of 5 containing functions with the property: If/'(z)l O, jzl < 1. In particular, we prove that the conjecture holds with 5?…
Some Radius Results for Univalent Functions
- F. Rønning
- Mathematics
- 15 August 1995
Abstract This paper deals with the geometrically motivated properties uniform starlikeness, uniform convexity and starlikeness with respect to symmetrical points. We give sharp radius results for…
Integral transforms of functions with the derivative in a halfplane
- S. Ponnusamy, F. Rønning
- Mathematics
- 1 December 1999
AbstractLetA be the class of normalized analytic functions in the unit disk Δ and define the class
$$\mathcal{P}_\beta = \left\{ {f \in \mathcal{A}|\exists \alpha \in \mathbb{R}|\operatorname{Re} \{…
Radius of Convexity and Radius of Starlikeness for Some Classes of Analytic Functions
- V. Ravichandran, F. Rønning, T. N. Shanmugam
- Mathematics
- 1 August 1997
This paper deals with the properties convexity and starlikeness of order α, uniform convexity, and a special type of starikeness that in a natural way corresponds to uniform convexity. We are…
Entering the mathematical register through evolution of the material milieu for classification of polygons
- F. Rønning, Heidi Strømskag
- Computer Science
- 1 February 2017
From classroom observations from Norway with 7-8 years old children working on geometrical shapes, it is concluded that certain challenges in the children's development of scientific terms to some extent are connected to specific semantic features of the Norwegian language.
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