q extension of Wielandt's Theorem

It is well known that the q-Gamma function cannot be characterised by its functional equation o q ( z + 1) =/((1 m q z )(1 m q )) o q ( z ) and the condition o q (1) = 1. In 1980 Richard Askey showed in [1] that the additional assumption of logarithmic convexity yields the uniqueness of o q ( x ) for real x > 0. The goal of this note is to establish a q-extension of Wielandt's theorem which gives a characterization of o q ( z ) for all $ z\in \{z\in{\shadC}:{\rm Re}(z)\gt 0\} $ .     

Some Remarks on the Principal Value Kernel in R m

It is shown how Clifford analysis offers a natural framework for defining the principal value kernel in euclidean m -dimensional space. Some elegant generalizations of classical formulae on the real line are obtained.     

Differential Operator Solutions of the Bauer-Peschl Equation

In this paper new solutions of the Bauer-Peschl equation represented by differential operators are derived. A relation to the solutions of Bauer is given. Furthermore, it will be said in which new way Bauer's solutions can be obtained. Also three other ways for obtaining the solutions of the Bauer-Peschl equation are sketched.     

Differential Inequalities and Starlike Functions

We develop sufficient conditions for various types of starlikeness for functions analytic in the unit disk. The problems that we consider are more general than similar problems considered by previous authors. Furthermore we obtain stronger estimates than in earlier works and in several cases sharp ones.     

Weighted Harmonic Bloch Spaces and Gleason's Problem

The harmonic function spaces are considered on the unit ball, which unify the Bloch space ( s = 1) and the Lipschitz spaces (0 < s < 1). This article presents a characterization of when s > 1 and gives a solution of Gleason's problem in for any s > 0.     

Lipschitzian Operators of Substitution in the Algebra ΛBV

We present necessary and sufficient conditions on the generating functions of operators of substitution (=Nemytskii superposition operators), which map the Waterman space v BV of functions of v -bounded variation on the interval into another space of this type and satisfy the Lipschitz condition.     

Fractal Interpolation Surfaces derived from Fractal Interpolation Functions

Based on the construction of Fractal Interpolation Functions, a new construction of Fractal Interpolation Surfaces on arbitrary data is presented and some interesting properties of them are proved. Finally, a lower bound of their box counting dimension is provided.     

Category Theoretic Properties of Topological Structures and Proximity Structures on L-fuzzy Space

This paper formulates the category of L-fuzzy spaces and fuzzy functions. It shows that the category of topological spaces and continuous fuzzy functions is a direct generalization of TOP and LTOP Moreover, it defines the concept of proximity space on L-fuzzy space and introduces its fundamental properties. A comparison between the classical case and the ordinary case has been outlined.     

On a result of Aumann and Shapley about values of non-atomic games

We focus our attention on the argument developed by R.J. Aumann and L.S. Shapley in a proposition used to prove the existence of a value on a certain class of games. Since we have found such an argument to be inexact, we have devised a supplementary construction which should be incorporated in the original proof to make it run in a satisfactory way.