Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 8 (2013), 11 -- 21

BOUNDED LINEAR OPERATORS ON FINITE DIMENSIONAL PROBABILISTIC NORMED SPACES

Mahmood Haji Shaabani and Mohammad Baseri Nezhad

Abstract. Probabilistic normed spaces were introduced by Serstnev and have been redefined by Alsina, Schweizer, and Sklar. In this paper, we obtain some conditions under which linear operators on finite dimensional probabilistic normed spaces are bounded and continuous.

2010 Mathematics Subject Classification: 54E70; 46S50.
Keywords: Probabilistic normed space; Serstnev space; D-bounded; Bounded operator.

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M. Haji Shaabani M. Baseri Nezhad
Shiraz University of Technology, Shiraz University of Technology,
Department of Mathematics, Department of Mathematics,
Faculty of Basic Sciences, Faculty of Basic Sciences,
P. O. Box 71555-313, Shiraz, P. O. Box 71555-313, Shiraz,
Iran. Iran.
e-mail: shaabani@sutech.ac.ir e-mail: m.baserinezhad@sutech.ac.ir

http://www.utgjiu.ro/math/sma