Journal of Inequalities and Applications 
Volume 2 (1998), Issue 1, Pages 37-55
doi:10.1155/S1025583498000022

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

Abstract

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.