On Some 2-banach Spaces 1

The main aim of this article is to introduce some difference sequence spaces with elements in a finite dimensional 2-normed space and extend the notion of 2-norm and derived norm to thus constructed spaces. We investigate the spaces under the action of different difference operators and show that these spaces become 2-Banach spaces when the base space is a 2-Banach space. We also prove that convergence and completeness in the 2-norm is equivalent to those in the derived norm as well as show that their topology can be fully described by using derived norm. Further we compute the 2-isometric spaces and prove the Fixed Point Theorem for these 2-Banach spaces. 2010 Mathematics Subject Classification: 40A05, 46A45, 46B70.