Superfractality of the set of incomplete sums of one positive series

• Date: 2018
• Main Authors: Markitan, V. P., Pratsiovytyi, M. V., Savchenko, I. O., Маркітан, В. П., Працьовитий, М. В., Савченко, І. О.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2018
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1644
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider a family of convergent positive normed series with real terms defined by the conditions $$\sum ^{\infty}_{n=1} d_n = \underbrace{c_1 + ...+c_1}_{a_1} + \underbrace{c_2 + ...+c_2}_{a_2} + ... + \underbrace{c_n + ...+c_n}_{a_n} + \widetilde{ r_n} = 1,$$ where $(a_n)$ is a nondecreasing seq...