The Completion of Generalized 2-Inner Product Spaces

Safa L.  Hamad; Zeana Z.  Jamil

doi:10.30526/36.1.2952

Authors

Safa L. Hamad Department of Mathematics , College of Sciences, University of Baghdad- Iraq.
Zeana Z. Jamil Department of Mathematics , College of Sciences, University of Baghdad- Iraq.

DOI:

https://doi.org/10.30526/36.1.2952

Keywords:

b-Cauchy Sequence, Equivalent Class, Metric space, Completion Generalized 2-Inner Product Space.

Abstract

A complete metric space is a well-known concept. Kreyszig shows that every non-complete metric space can be developed into a complete metric space , referred to as completion of .

We use the b-Cauchy sequence to form which “is the set of all b-Cauchy sequences equivalence classes”. After that, we prove to be a 2-normed space. Then, we construct an isometric by defining the function from to ; thus and are isometric, where is the subset of composed of the equivalence classes that contains constant b-Cauchy sequences. Finally, we prove that is dense in , is complete and the uniqueness of is up to isometrics

Author Biographies

Safa L. Hamad, Department of Mathematics , College of Sciences, University of Baghdad- Iraq.
Zeana Z. Jamil, Department of Mathematics , College of Sciences, University of Baghdad- Iraq.

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