ŞÜKRAN KONCA, HENDRAGUNAWAN, METİNBAŞARIR

SOME REMARKS ON L^p AS AN n-NORMED SPACE

As in 2-normed spaces, we can also give two definitions for Cauchysequences in n-normed spaces. It is known that in some cases, especially in thefinite dimensional case and the standard case, two definitions are equivalent.What is not clear is in the infinite dimensional case. In this paper, we willprove that these two definitions are still equivalent inpspace

Keywords:

2-norm; n-norm; Cauchy sequence; convergence; the space of psummable sequences,

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Department of Mathematics, Bitlis Eren University, 13000, Bitlis, Turkey
E-mail address: skonca@beu.edu.tr 2 Department of Mathematics, Institute of Technology Bandung, 40132, Bandung, Indonesia
E-mail address: hgunawan@math.itb.ac.id 3 Department of Mathematics, Sakarya University, 54187, Sakarya, Turkey
E-mail address: basarir@sakarya.edu.tr