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On two new functional equations for generalized Joukowski transformations

M. Baran, H. Haruki (1991)

Annales Polonici Mathematici

The purpose of this paper is to solve two functional equations for generalized Joukowski transformations and to give a geometric interpretation to one of them. Here the Joukowski transformation means the function 1 / 2 ( z + z - 1 ) of a complex variable z.

On zeros of differences of meromorphic functions

Yong Liu, HongXun Yi (2011)

Annales Polonici Mathematici

Let f be a transcendental meromorphic function and g ( z ) = f ( z + c ) + + f ( z + c k ) - k f ( z ) and g k ( z ) = f ( z + c ) f ( z + c k ) - f k ( z ) . A number of results are obtained concerning the exponents of convergence of the zeros of g(z), g k ( z ) , g(z)/f(z), and g k ( z ) / f k ( z ) .

On ω-convex functions

Tomasz Szostok (2011)

Banach Center Publications

In Orlicz spaces theory some strengthened version of the Jensen inequality is often used to obtain nice geometrical properties of the Orlicz space generated by the Orlicz function satisfying this inequality. Continuous functions satisfying the classical Jensen inequality are just convex which means that such functions may be described geometrically in the following way: a segment joining every pair of points of the graph lies above the graph of such a function. In the current paper we try to obtain...

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