IJPAM: Volume 21, No. 2 (2005)
BEST APPROXIMATION IN A CLASS OF
ORDERED NORMED SPACES WITHOUT
A PRE-ORDER RELATION
ORDERED NORMED SPACES WITHOUT
A PRE-ORDER RELATION
H. Mohebi
, H. Sadeghi
Department of Mathematics
University of Kerman
Kerman, IRAN
e-mail: hmohebi@mail.uk.ac.ir
e-mail: hsadeghi@graduate.uk.ac.ir
, H. Sadeghi
Department of Mathematics
University of Kerman
Kerman, IRAN
e-mail: hmohebi@mail.uk.ac.ir
e-mail: hsadeghi@graduate.uk.ac.ir
Abstract.We examine best approximation by closed sets in a class of ordered normed spaces with a relation which is not necessarily a pre-order relation. We use downward and upward sets as tools for examination of best approximation by closed sets. We first study best approximation properties of these sets.
Received: April 10, 2005
AMS Subject Classification: 41A65, 46B40, 41A50
Key Words and Phrases: best approximation, downward set, upward set, relatively downward set, relatively upward set, proximinal set
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 2
