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On ( j , k ) -symmetrical functions

Piotr LiczberskiJerzy Połubiński — 1995

Mathematica Bohemica

n the present paper the authors study some families of functions from a complex linear space X into a complex linear space Y . They introduce the notion of ( j , k ) -symmetrical function ( k = 2 , 3 , ; j = 0 , 1 , , k - 1 ) which is a generalization of the notions of even, odd and k -symmetrical functions. They generalize the well know result that each function defined on a symmetrical subset U of X can be uniquely represented as the sum of an even function and an odd function.

Applications of the Hadamard product in geometric function theory

Zbigniew Jerzy JakubowskiPiotr LiczberskiŁucja Żywień — 1991

Mathematica Bohemica

Let 𝒜 denote the set of functions F holomorphic in the unit disc, normalized clasically: F ( 0 ) = 0 , F ' ( 0 ) = 1 , whereas A 𝒜 is an arbitrarily fixed subset. In this paper various properties of the classes A α , α C { - 1 , - 1 2 , ... } , of functions of the form f = F * k α are studied, where F . A , k α ( z ) = k ( z , α ) = z + 1 1 + α z 2 + ... + 1 1 + ( n - 1 ) α z n + ... , and F * k α denotes the Hadamard product of the functions F and k α . Some special cases of the set A were considered by other authors (see, for example, [15],[6],[3]).

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