The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Power and Euler-Lagrange Norms


Mohammad Sal Moslehian and John Michael Rassias

Department of Mathematics,
Ferdowsi University,
P. O. Box 1159, Mashhad 91775,
Department of Pure Mathematics,
University of Leeds,
Leeds LS2 9JT,
United Kingdom.

Pedagogical Department, E.E., Section of Mathematics and Informatics
National and Capodistrian University of Athens,
4, Agamemnonos str., Aghia Paraskevi, Attikis 15342, Athens,


We introduce the notions of power and Euler-Lagrange norms by replacing the triangle inequality, in the definition of norm, by appropriate inequalities. We prove that every usual norm is a power norm and vice versa. We also show that every norm is an Euler-Lagrange norm and that the converse is true under certain condition.

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