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About differentiability and V BG * class

Turowska M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2014

Vol. 19

245--249

Let X be a finite dimensional real Banach space. We show that if the contingent of the curve Γ : (a, b) → X fulfils some conditions then each parametrization of that curve is V BG * . Stanisław Saks proved that each V BG * function is differentiable at a set of full Lebesgue measure. The result of this paper is a partial converse of that theorem.

Mean-value theorems for one-sided differentiable functions

Wituła R., Hetmaniok E., Słota D.

Fasciculi Mathematici

2012

Nr 48

145--154

We show that Kubik's generalizations of the classical mean-value theorems for one-sided differentiable functions are equivalent to those of Karamata and Vučkovič. Some applications of these theorems are presented.

On some extremal problem of chosen two-parametrical families of real functions

Wrzesień A.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

Vol. 7, nr 2

97-105

In this paper we continue the investigation from [1]. There we have considered the case of the circle and the ellipse. Now we will take two-parametrical families of differentiable functions. For these families we determine extremality coefficients. In the last part of this paper we study the case of functions of two variables.