IJPAM: Volume 68, No. 1 (2011)



Gauhati University
Kokrajhar Campus, Assam, INDIA
e-mail: [email protected]

Post Graduate College of Science - PGCS, Saifabad
Osmania University
Hyderabad, 500004, AP, INDIA
e-mail: [email protected]
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.
Received: October 22, 2009
AMS Subject Classification: 40A05, 46A45, 46B70
Key Words and Phrases: -normed spaces, completeness, fixed point theorem
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 68
Issue: 1