التفاصيل البيبلوغرافية
| العنوان: |
ONE CLASS OF CONTINUOUS FUNCTIONS WITH COMPLICATED LOCAL PROPERTIES RELATED TO ENGEL SERIES. |
| المؤلفون: |
BARANOVSKYI, OLEKSANDR, PRATSIOVYTYI, MYKOLA |
| المصدر: |
Functiones et Approximatio Commentarii Mathematici; Jun2023, Vol. 68 Issue 2, p143-162, 20p |
| مصطلحات موضوعية: |
CONTINUOUS functions, DIFFERENTIABLE functions, SET functions, MONOTONIC functions |
| مستخلص: |
In the paper, we construct and study the class of continuous on [0, 1] functions with continuum set of peculiarities (singular, nowhere monotonic, and non-differentiable functions are among them). The representative of this class is the function y = f(x) defined by the Engel representation of argument: x = 1X n=1 1 (2 + g1)(2 + g1 + g2) . . . (2 + g1 + g2 + . . . + gn) =: Eg 1g2...gn..., where gn = gn(x) 2 {0, 1, 2, . . .}, and convergent real series 1X n=0 un = u0 + u1 + . . . + un + rn = 1, |un| < 1, 0 < rn < 1, by the following equality f(Eg 1(x)g2(x)...gn(x)...) = rg1(x) + 1X k=2 - rgk(x) kY-1 i=1 ugi(x). We study local and global properties of function f: structural, extremal, differential, integral, and fractal properties. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
Complementary Index |
