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Warianty tytułu
Języki publikacji
Abstrakty
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.
Rocznik
Tom
Strony
49--60
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Emerytowany pracownik Akademii Pomorskiej w Słupsku
Bibliografia
- [1] Bruckner A. M., An affirmative answer to a problem of Zahorski, Mich. Math. Journ. 13 (1966), p. 15–26.
- [2] Goldovski G., Note sur les dérivées éxactes, Rec. Math. Soc. Math. Moscou 35 (1928), p. 35–36.
- [3] Jedrzejewski J. M., O monotonicznosci funkcji, Master Thesis, Łódz University (1969).
- [4] Leonard J. L., Some conditions implying the monotonicity of a real function, Rev. Roum. Math. Pures et Appl., 12 (1972), p. 757–780.
- [5] O’Malley R. J., Selective derivatives, Acta Math. Acad. Sci. Hung., 29 (1977), p. 77–97.
- [6] Mastalerz-Wawrzynczak M., On a certain condition of the monotonicity of functions, Fund. Math. XCVII (1977), p. 188–198.
- [7] Saks S., Theory of the integral, Monografie Matematyczne 7, Warszawa–Lwów, 1937.
- [8] Swiatkowski T., On the conditions of monotonicity of functions, Fund. Math. 59, (1966), p. 189–201.
- [9] Swiatkowski T., On a certain generalization of the notion of the derivative, Zesz. Nauk. P. Ł. 149, Matematyka 2.1 (1972), p. 89–103. (in Polish).
- [10] Tolstov G., Sur quelques propriétés des fonctions approximativement continues, Rec. Math. N. S. 5 (1939), p. 637–645. (Mat. Sb.)
- [11] Thomson B. S., Real Functions, Lectures Notes in Mathematics, No 1170, Springer Verlag, Berlin-Heidelberg-New York-Tokyo 1985.
- [12] Tonelli L., Sulle derivate esatte, Mem. Inst. Bologna (8) 8 (1930-31), p. 13–15.
- [13] Zahorski Z., Sur la première dérivée Trans. Amer. Math. Soc. 69 (1950), p. 1–54.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e2e1b64c-c44d-426b-a1ae-758ad8738b2e