A Survey on Cauchy-Bunyakovsky-Schwarz Type Discrete Inequalities

Volume 4, Issue 3 (GI8), 2003

Article 63

A SURVEY ON CAUCHY-BUNYAKOVSKY-SCHWARZ TYPE DISCRETE INEQUALITIES

SCHOOL OF COMPUTER SCIENCE AND MATHEMATICS
VICTORIA UNIVERSITY OF TECHNOLOGY
PO BOX 14428
MELBOURNE CITY MC
VICTORIA 8001, AUSTRALIA.
E-Mail: sever@csm.vu.edu.au

Received 22 January, 2003; Accepted 14 May, 2003.
Communicated by: P.S. Bullen

ABSTRACT. The main purpose of this survey is to identify and highlight the discrete inequalities that are connected with (CBS)- inequality and provide refinements and reverse results as well as to study some functional properties of certain mappings that can be naturally associated with this inequality such as superadditivity, supermultiplicity, the strong versions of these and the corresponding monotonicity properties. Many companion, reverse and related results both for real and complex numbers are also presented.

Key words:
Cauchy-Bunyakovsky-Schwarz inequality, Discrete inequalities.

2000 Mathematics Subject Classification:
26D15, 26D10.

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