The Koebe Domain for Concave Univalent Functions

2000 Mathematics Subject Classification: 30C25, 30C45.

On the Residuum of Concave Univalent Functions

2000 Mathematics Subject Classification: 30C25, 30C45.

Locally univalent functions, VMOA, and the Dirichlet space

"Vegeu el resum a l'inici del document del fitxer adjunt."

Alternative Characterization of the Class k-UCV and Related Classes of Univalent Functions

In this paper an alternative characterization of the class of functions called k -uniformly convex is found. Various relations concerning connections with other classes of univalent functions are given. Moreover a new class of univalent functions, analogous to the ’Mocanu class’ of functions, is introduced. Some results concerning this class are derived.

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Some Notes about a Class of Univalent Functions with Negative Coefficients

MSC 2010: 30C45, 30C50

A Note on Univalent Functions with Finitely many Coefficients

MSC 2010: 30C45

On a Class of Univalent Functions with Negative Coefficients

Донка Пашкулева - Предмет на тази статия е получаването на точни оценки за коефициентите и ръста на функциите за някои класове еднолистни функции с отрицателни коефициенти.

Application of Salagean and Ruscheweyh Operators on Univalent Holomorphic Functions with Finitely many Coefficients

MSC 2010: 30C45, 30C50

Bieberbach's Conjecture, the de Branges and Weinstein Functions and the Askey-Gasper Inequality

The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach in 1916 [Bieberbach1916]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function which maps the unit disk onto a radially slit plane. The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Louis de Branges in 1984 [deBranges1985] when some experts were rather trying to disprove it. It turned out that an inequality of Askey and Gasper [AskeyGasper1976] about certain hypergeometric functions played a crucial role in de Branges' proof. In this article I describe the historical development of the conjecture and the main ideas that led to the proof. The proof of Lenard Weinstein (1991) [Weinstein1991] follows, and it is shown how the two proofs are interrelated. Both proofs depend on polynomial systems that are directly related with the Koebe function. At this point algorithms of computer algebra come into the play, and computer demonstrations are given that show how important parts of the proofs can be automated.

Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions

2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

MSC2010: 30C45, 33C45

Stochastic dominance and absolute risk aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

Efficient interval scoring rules

Scoring rules that elicit an entire belief distribution through the elicitation of point beliefsare time-consuming and demand considerable cognitive e¤ort. Moreover, the results are validonly when agents are risk-neutral or when one uses probabilistic rules. We investigate a classof rules in which the agent has to choose an interval and is rewarded (deterministically) onthe basis of the chosen interval and the realization of the random variable. We formulatean e¢ ciency criterion for such rules and present a speci.c interval scoring rule. For single-peaked beliefs, our rule gives information about both the location and the dispersion of thebelief distribution. These results hold for all concave utility functions.