Recent zbMATH articles in MSC 41A30https://www.zbmath.org/atom/cc/41A302022-05-16T20:40:13.078697ZWerkzeugThe discrete case of the mixed joint universality for a class of certain partial zeta-functionshttps://www.zbmath.org/1483.111912022-05-16T20:40:13.078697Z"Kačinskaitė, Roma"https://www.zbmath.org/authors/?q=ai:kacinskaite.roma"Matsumoto, Kohji"https://www.zbmath.org/authors/?q=ai:matsumoto.kohjiAuthors' abstract: We give a new type of mixed discrete joint universality properties, which is satisfied by a wide class of zeta-functions. We study the universality for a certain modification of Matsumoto zeta-functions \(\varphi_h(s)\) and a collection of periodic Hurwitz zeta-functions \(\zeta (s;\alpha;\mathfrak B)\) under the condition that the common difference of arithmetical progression \(h > 0\) is such that \(\exp \{ \frac{2\pi}h\}\) is a rational number and parameter \(\alpha\) is a transcendental number.
Reviewer: Anatoly N. Kochubei (Kyïv)Joint discrete universality for periodic zeta-functions. IIIhttps://www.zbmath.org/1483.111972022-05-16T20:40:13.078697Z"Laurinčikas, Antanas"https://www.zbmath.org/authors/?q=ai:laurincikas.antanasSummary: In the paper, a joint theorem on the approximation of collections of analytic functions by generalized discrete shifts of zeta-functions with periodic coefficients is obtained. The latter result extend theorems of [Part I, Zbl 1441.11235].
For Part I and II, see [ibid. 42, No. 5, 687--699 (2019; Zbl 1441.11235); ibid. 43, No. 12, 1765--1779 (2020; Zbl 1457.11125)].Box-counting dimension and analytic properties of hidden variable fractal interpolation functions with function contractivity factorshttps://www.zbmath.org/1483.410012022-05-16T20:40:13.078697Z"Yun, CholHui"https://www.zbmath.org/authors/?q=ai:yun.cholhui"Ri, MiGyong"https://www.zbmath.org/authors/?q=ai:ri.mi-gyongSummary: We estimate the bounds for box-counting dimension of hidden variable fractal interpolation functions (HVFIFs) and hidden variable bivariate fractal interpolation functions (HVBFIFs) with four function contractivity factors and present analytic properties of HVFIFs which are constructed to ensure more flexibility and diversity in modeling natural phenomena. Firstly, we construct the HVFIFs and analyze their smoothness and stability. Secondly, we obtain the lower and upper bounds for box-counting dimension of the HVFIFs. Finally, in the similar way, we get the lower and upper bounds for box-counting dimension of HVBFIFs in [\textit{C.-H. Yun} and \textit{M.-K. Ri}, Asian-Eur. J. Math. 12, No. 2, Article ID 1950021, 15 p. (2019; Zbl 1409.28003)].