IJPAM: Volume 94, No. 2 (2014)
Marcin Szweda, Roman Wituła
Institute of Mathematics
Silesian University of Technology
Kaszubska 23, 44-100 Gliwice, POLAND
Abstract. Wituła and Słota have distinguished two new subfamilies and of the classical spaces , of absolutely -summable sequences (the first one is called the almost , the second one - the exactly ), for every . In presented paper the new properties of families and , connected with some infinite subfamilies of , are introduced.
We also prove that if for an increasing sequence of positive integers
denotes the number of not exceeding , i.e. denotes the counting function
of sequence , and possesses the Chebyshev estimation
(like for the prime numbers) then
Received: May 4, 2014
AMS Subject Classification: 40A05, 46A99
Key Words and Phrases: almost , exactly , counting function, prime number theorem
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DOI: 10.12732/ijpam.v94i2.11 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 241 - 250
This work is licensed under the Creative Commons Attribution International License (CC BY).