IJPAM: Volume 74, No. 4 (2012)

RESULTS IN LINEAR 2-NORMED SPACES ANALOGOUS
TO BAIRE'S THEOREM AND CLOSED GRAPH THEOREM

Raji Pilakkat$^1$, Sivadasan Thirumangalath$^2$
Department of Mathematics
University of Calicut
Kerala, 673635, INDIA


Abstract. In this paper, the Baire's theorem for 2-Banach spaces is proved. The concept of continuous functions on linear 2- normed spaces is introduced and some relations between continuity and boundedness of linear functions are established. The result for a linear 2-normed space analogous to the closed graph theorem is proved.

Received: November 11, 2011

AMS Subject Classification: 46A03, 46A30

Key Words and Phrases: linear 2-normed space, 2-Banach space, Baires theorem, closed graph theorem

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 74
Issue: 4