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Around the Świątkowski-type conditions

Filipczak Małgorzata, Terepeta Małgorzata

Journal of Applied Analysis

2023

Vol. 29, nr 2

205--217

In this paper, we will focus on different types of Świątkowski conditions: Świątkowski, strong Świątkowski and weak Świątkowski conditions. We present the main properties of the families of functions fulfilling such conditions.

Maximal classes for lower and upper semicontinuous strong Świątkowski functions

Szczuka P.

Demonstratio Mathematica

2014

Vol. 47, nr 1

48--55

In this paper, we characterize the maximal additive and multiplicative classes for lower and upper semicontinuous strong Świątkowski functions and lower and upper semicontinuous extra strong Świątkowski functions. Moreover, we characterize the maximal class with respect to maximums for lower semicontinuous strong Świątkowski functions and lower and upper semicontinuous extra strong Świątkowski functions.

Maximums of upper semicontinuous strong Świątkowski functions

Szczuka P.

Demonstratio Mathematica

2011

Vol. 44, nr 1

59-65

In this paper we characterize the family of the maximums of upper semicontinuous strong Świątkowski functions and we show that the family of all upper semicontinuous strong Świątkowski functions is not closed with respect to maximums.

Products of strong Świątkowski functions

Szczuka P.

Journal of Applied Analysis

2006

Vol. 12, nr 1

129-145

In this paper we characterize the products of four or more strong Świątkowski functions.