PUBLICATIONS DE L'INSTITUT MATH\'EMATIQUE (BEOGRAD) (N.S.) EMIS ELibM Electronic Journals Publications de l'Institut Mathématique (Beograd)
Vol. 73(87), pp. 149-154 (2003)

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ON GENERALIZED INEQUALITIES OF HEINZ, HALMOS AND BERNSTEIN

C.-S. Lin

Department of Mathematics, Bishop's University, Lennoxville, Quebec, J1M 1Z7 Canada

Abstract: We present generalized inequalities of Heinz, Halmos and Bernstein. It is proved that they are all equivalent to one another. In fact they are are all equivalent to the Cauchy--Schwarz inequality. Equality condition and the bound of inequality are established.

Classification (MSC2000): 47A63; 47A30

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