Journal of Inequalities and Applications
Volume 2 (1998), Issue 1, Pages 37-55

The mapping vx,y in normed linear spaces with applications to inequalities in analysis

S. S. Dragomir1 and J. J. Koliha2

1Department of Mathematics, University of Transkei, Unitra, Umtata 5100, South Africa
2Department of Mathematics and Statistics, University of Melbourne, Parkville 3052, Australia

Received 19 August 1996

Copyright © 1998 S. S. Dragomir and J. J. Koliha. 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.


In this paper we introduce the mapping vx,y connected with the lower and upper semiinner products (,)i and (,)s , and study its monotonicity, boundedness, convexity and other properties. Applications to theory of inequalities in analysis are given including refinements of the Schwarz inequality.