Certain multiplier version of the Riemann derangement theorem

• Autorzy: Wituła R.
• Języki publikacji: EN

Abstrakty

EN

Aim of this paper is to consider a problem formulated in [6]. Namely, it has been proven that for any sequences {xn} (…) , for every interval (…) , there exist a nondecreasing sequence (…) of positive integers and a sequence (…) signs such that the set of limit points of the series (…) is equal to [a, b].

Słowa kluczowe

EN

Riemann derangement theorem

PL

twierdzenie Riemanna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 1
• Strony: 125--129
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Wituła R.

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

Bibliografia

• [1] R. Filipów, P. Szuca, Rearrangement of conditionally convergent series on a small set, J. Math. Anal. Appl. 362 (2010), 64–71.
• [2] F. Prus-Wisniowski, Two refinements of the Riemann Derangement Theorem, in: “Real Functions, Density Topology and Related Topics”. A volume dedicated to W. Wilczynski (ed. M. Filipczak & E. Wagner-Bojakowska), Łódz University Press, Łódz 2011, 165–172.
• [3] W. Wilczynski, On the Riemann derangement theorem, Słupskie Prace Mat.-Fiz. 4 (2007), 79–82.
• [4] R. Wituła, On the set of limit points of the partial sums of series rearranged by a given divergent permutation, J. Math. Anal. Appl. 362 (2010), 542–552.
• [5] R. Wituła, The Riemann Derangement Theorem and Divergent Permutations, Tatra Mountains Math. Publ. (in press).
• [6] R. Wituła, E. Hetmaniok, D. Słota, Some variation on the Riemann Derangement Theorem, Tatra Mountains Math. Publ. (in press).