Further inequalities related to the Schwarz inequality in real or complex inner product spaces are given.

Reprints available directly from the publisher Photocopying permitted by license only (C) 1999 OPA (Overseas Publishers Association) N.V. In our preceding note, we discussed a generalized Schwarz inequality, an improvement of the Heinz-Kato-Furuta inequality and an inequality related to the Furuta inequality. In succession, we give further discussions on them from the viewpoint of the covarianc...

Recent reverses for the celebrated Schwarz inequality in inner product spaces and applications for discrete and integral inequalities are surveyed.

The purpose of this research paper is to introduce new Cauchy–Schwarz inequalities that are valid in semi-Hilbert spaces, which generalizations Hilbert spaces. We demonstrate how these can be employed derive novel A-numerical radius inequalities, where A denotes a positive semidefinite operator complex space. Some our expand upon the existing literature on numerical with space operators, import...

We establish conditions under which the extended Hardy-Littlewood inequality ∫ RN H ( |x|, u1(x), . . . , um(x) ) dx ≤ ∫ RN H ( |x|, u1(x), . . . , um(x) ) dx, where each ui is non-negative and u ∗ i denotes its Schwarz symmetrization, holds. We also determine appropriate monotonicity assumptions on H such that equality occurs in the above inequality if and only if each ui is Schwarz symmetric....

Inequalities are ubiquitous in Mathematics (and in real life). For example, in optimization theory (particularly in linear programming) inequalities are used to described constraints. In analysis inequalities are frequently used to derive a priori estimates, to control the errors and to obtain the order of convergence, just to name a few. Of particular importance inequalities are Cauchy-Schwarz...