Double Series and Sums

• Autorzy: Noboru Endou
• Języki publikacji: EN

Abstrakty

EN

In this paper the author constructs several properties for double series and its convergence. The notions of convergence of double sequence have already been introduced in our previous paper [18]. In section 1 we introduce double series and their convergence. Then we show the relationship between Pringsheim-type convergence and iterated convergence. In section 2 we study double series having non-negative terms. As a result, we have equality of three type sums of non-negative double sequence. In section 3 we show that if a non-negative sequence is summable, then the sequence of rearrangement of terms is summable and it has the same sums. In the last section two basic relations between double sequences and matrices are introduced.

Słowa kluczowe

EN

double series

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2014
• Tom: 22
• Numer: 1
• Strony: 57-68

Twórcy

autor

Noboru Endou

• Gifu National College of Technology Gifu, Japan

Bibliografia

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Identyfikatory

DOI

10.2478/forma-2014-0006