# IJPAM: Volume 68, No. 1 (2011)

ON NON-STANDARD n-NORM ON SOME SEQUENCE SPACES

Hemen Dutta, B. Surender Reddy
Department of Mathematics
Gauhati University
Kokrajhar Campus, Assam, INDIA
e-mail: hemen_dutta08@rediffmail.com
Department of Mathematics
Osmania University
e-mail: bsrmathou@yahoo.com

Abstract. In this paper, we construct some difference sequence spaces which we call the spaces of -convergent, -null and -bounded sequences with respect to -norm on a real linear space . We study these spaces by defining non-standard -norm and -norm for every . We show that under certain cases, convergence and completeness in the -norm is equivalent to those in the -norm. We also prove the fixed point theorem for these spaces, which are -Banach spaces.