@MISC{DBLSEQ_2.MIZ,
  AUTHOR = {Endou, Noboru},
  TITLE = {Double Series and Sums},
  DAY = {31},
  MONTH = {March},
  YEAR = {2014},
  SECTION1 = {Double Series and Their Convergence},
  SECTION2 = {Double Series of Non-negative Double Sequence},
  SECTION3 = {Summability for Rearrangements of Non-negative Real Sequence},
  SECTION4 = {Basic Relations between Double Sequences and Matrices},
  ADDRESS1 = {Gifu National College of Technology\\2236-2 Kamimakuwa, Motosu, Gifu, Japan},
  SUMMARY = {In this paper the author constructs several properties for double series and
  its convergence. The notions of convergence of double sequence already has been introduced
  in our previous paper \cite{DBLSEQ_1.ABS}. 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 squence 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.},
  NOTE = {This work was supported by JSPS KAKENHI 23500029.}}
