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Journal of Function Spaces
Volume 2015, Article ID 945758, 3 pages
Research Article

Inequalities Characterizing Linear-Multiplicative Functionals

Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland

Received 14 October 2014; Accepted 13 January 2015

Academic Editor: Bruce A. Watson

Copyright © 2015 Włodzimierz Fechner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove, in an elementary way, that if a nonconstant real-valued mapping defined on a real algebra with a unit satisfies certain inequalities, then it is a linear and multiplicative functional. Moreover, we determine all Jensen concave and supermultiplicative operators , where and are compact Hausdorff spaces.