Warianty tytułu
Języki publikacji
Abstrakty
The study shows that the functional equation f (f (x)) = ln(1 + x) has a unique result in a semigroup of power series with the intercept equal to 0 and the function composition as an operation. This function is continuous, as per the work of Paulsen [2016]. This solution introduces into statistics the law of the one-and-a-half logarithm. Sometimes the natural growth processes do not yield to the law of the logarithm, and a double logarithm weakens the growth too much. The law of the one-and-a-half logarithm proposed in this study might be the solution.(original abstract)
Twórcy
autor
- Wrocław University of Economics, Poland
autor
- Wrocław University of Economics, Poland
Bibliografia
- Bödewadt U.T. (1944). Reeller Funktionen zur Iteration. Math. Z. 49, pp. 497-516.
- Iga K. Continuous half-iterates of functions. Manuscript. URLs or http://math.stan-ford.edu/~iga http://math.pepperdine.edu/kiga/Papers/halfiter.ps.
- Kneser H. (1950). Reelle analytische Lösungen der Gleichung 𝜓𝜓𝜓𝜓(𝑥𝑥)=𝑒𝑒𝑥𝑥 und verwand-ter Funktionalgleichungen. Journal für die reine und angewandte Mathematik 187, pp. 56-67.
- KuczmaM. (1969). Fractional iteration of differentiable functions. Annales Polonici Mathe-matici. Vol. 2. No. 22, pp. 217-227.
- Paulsen W. (2016). Finding the natural solution to 𝑓𝑓(𝑓𝑓(𝑥𝑥))=𝑒𝑒𝑥𝑥. The Korean Journal of Mathematics 24 (1), pp. 81-106.
- Zhang W. (1997). PM functions. Their characteristic intervals and iterative roots. Annales Polonici Mathematici. Vol. 2. No. 65, pp. 119-128.
- Zubrzycki S. (1962). Wzór rekurencyjny dla ilości partycji ograniczonych. Applicationes Mathematica 6 (2), pp. 231-234.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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