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3 Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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Asymmetry in real functions theory

Jędrzejewski J. M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2018

Vol. 23

11--24

Since the beginning of the XX century many authors considered characterizations of local properties for real functions of a real variable which have been defined as global properties. We present a short survey of local properties of the well known global ones and consider of how small/big the set of asymmetrical behaviour of a function must be.

On monotonicity of real functions

Jędrzejewski J. M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2017

Vol. 22

49--60

Monotonicity of functions were of great interest of many mathematicians. Starting from the well known theorem of monotonicity of a differentiable function one can get quite sophisticated results. We give a survey of results when thesis of them is continuous and monotone function. Someone can ask why it should be continuous. Even a differentiable functions but not at the only point of its domain with positive derivative need not be non-decreasing. That is why we want to look for theorems for continuous functions.

A mistake in definition of a limit of a function and some consequences

Jędrzejewski J. M., Kostrzewski T.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2014

Vol. 19

61--65

Many times our students make some errors in definitions, especially when we must apply some quantifiers. The definition of a limit is one of the definition with many quantifiers, so one can observe many mistakes in it. We want to present one of possible mistakes and show how to improve the understanding of this difficult but one of most important notions.