ON CERTAIN TOPOLOGICAL STRUCTURES OF 2- NORMED SPACE VALUED ORLICZ SPACE ï€ c0 ((S, ||.,.||), Φ, u– ) OF NULL SEQUENCES

Abstract

The aim of this paper is to   introduce   and study  a new  class   c₀ (( S, ||. , .||), F , )     of 2-normed space  valued vector sequences using Orlicz function as a generalization of the basic space c_{0 Â} of all  converging  sequences. Beside the  investigation pertaining to  the  linear space  structures of  the class  c₀ (( S, ||. , .||), F , )  with some  topological properties, our primarily interest is to explore the containment relation  of  the class  c₀ (( S, ||. , .||), F , )  in terms of different values of   .

 Keywords: Sequence space, Normal Space , 2- normed Space, Orlicz Function, Orlicz Space.

 2010 AMS Subject Classification: Primary - 46A45, Secondary - 46B 15