The Completion of Generalized 2-Inner Product Spaces

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