Mean-value theorems for one-sided differentiable functions

• Autorzy: Wituła R. , Hetmaniok E. , Słota D.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

mean value theorem; one-sided right and left derivatives; differentiable functions

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2012
• Tom: Nr 48
• Strony: 145--154
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Wituła R.

• Institute of Mathematics Silesian University of Technology Kaszubska 23, Gliwice 44-100, Poland

autor

Hetmaniok E.

• Institute of Mathematics Silesian University of Technology Kaszubska 23, Gliwice 44-100, Poland

autor

Słota D.

• Institute of Mathematics Silesian University of Technology Kaszubska 23, Gliwice 44-100, Poland

Bibliografia

• [1] Flett T.M., A mean value theorem, Math. Gazette, 42(1958), 38-39.
• [2] Goodner D.B., Mean value theorems for functions with finite derivates, Amer. Math. Monthly, 67(1960), 852-855.
• [3] Goodner D.B., An extended mean value theorem, Mathematics Magazine, 36(1)(1963), 15-16.
• [4] Hetmaniok E., Słota D., Wituła R., Mean Value Theorems, Wydawnictwo Politechniki Śląskiej, (in review, in Polish).
• [5] Karamata J., Sur la formule des accroissements finis, Srpska Akad. Nauka. Zbornik Radova, Mat. Inst., 1(1951), 119-124.
• [6] Kubik L., A characterization of the class L of probability distributions, Studia Math., 21(1962), 245-252.
• [7] Kubik L., Generalizations of the Rolle, Lagrange and Cauchy theorems, Wiadomości Matematyczne, tom V (1962), 47-51 (in Polish).
• [8] Lojasiewicz S., Introduction to the Real Functions Theory, PWN, Warsaw (1973) (in Polish).
• [9] Minassian D., A mean value theorem for one-sided derivatives, Amer. Math. Monthly, 114(2007), 28.
• [10] Minassian D., Necessary and sufficient conditions for a function to be convex, Amer. Math. Monthly, 114(2007), 39.
• [11] Trahan D.H., A new type of mean value theorem, Math. Magazine, 39(1966), 264-268.
• [12] Utz W.R., Mean value theorems for functions with left and right derivatives, Amer. Math. Monthly, 62(1955), 178-179.
• [13] Vuckovic V., Quelques extensions des theoremes de moyenne, Srpska Akad. Nauka. Zbornik Radova, Mat. Inst., 18(1952), 159-166.