The Completion of Generalized 2-Inner Product Spaces

Main Article Content

Safa L. Hamad
Zeana Z. Jamil


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


Article Details

How to Cite
Hamad, S. L. ., & Jamil, Z. Z. . (2023). The Completion of Generalized 2-Inner Product Spaces. Ibn AL-Haitham Journal For Pure and Applied Sciences, 36(1), 311–317.
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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