Fractal functions of exponential type that is generated by the $Q_2^*$-representation of argument - M.V. Pratsovytyi; Ya. V. Goncharenko; I. M. Lysenko; S.P. Ratushniak (Математичні Студії)
We consider function $f$ which is depended on the parameters $0<a\in R$, $q_{0n}\in (0;1)$, $n\in N$ and convergent positive series $v_1+v_2+...+v_n+...$, defined by equality $f(x=Δ^{Q_2^*}_{α_1α_2...α_n...})=a^{φ(x)}$, where $α_n\in \{0,1\}$, $φ(x=Δ^{Q_2^*}_{α_1α_2...α_n...})=α_1v_1+...+α_nv_n+...$, $q_{1n}=1-q_{0n}$, $Δ^{Q_2^*}_{α_1...α_n...}=α_1q_{1-α_1,1}+ \sum\limits_{n=2}^{∞}\big(α_nq_{1-α_n,n}\prod\limits_{i=1}^{n-1}q_{α_i,i}\big)$. In the paper we study structural, variational, integral, differential and fractal properties of the function $f$.