The Weighted Arithmetic Mean–Geometric Mean Inequality is Equivalent to the Hölder Inequality

The matrix arithmetic-geometric mean inequality revisited

Another View on the Hölder Inequality

Every diagonal matrix D yields an endomorphism on the n-dimensional complex vector space. If one provides the n with Hölder norms, we can compute the operator norm of D. We define homogeneous weighted spaces as a generalization of normed spaces. We generalize the Hölder norms for negative values, this leads to a proof of an extended version of the Hölder inequality. Finally, we formulate this v...

Hölder continuity of a parametric variational inequality

‎In this paper‎, ‎we study the Hölder continuity of solution mapping to a parametric variational inequality‎. ‎At first‎, ‎recalling a real-valued gap function of the problem‎, ‎we discuss the Lipschitz continuity of the gap function‎. ‎Then under the strong monotonicity‎, ‎we establish the Hölder continuity of the single-valued solution mapping for the problem‎. ‎Finally‎, ‎we apply these resu...

Best Upper Bounds Based on the Arithmetic-geometric Mean Inequality

In this paper we obtain a best upper bound for the ratio of the extreme values of positive numbers in terms of the arithmetic-geometric means ratio. This has immediate consequences for condition numbers of matrices and the standard deviation of equiprobable events. It also allows for a refinement of Schwarz’s vector inequality.

A Relationship between Subpermanents and the Arithmetic-Geometric Mean Inequality

Using the arithmetic-geometric mean inequality, we give bounds for k-subpermanents of nonnegative n × n matrices F. In the case k = n, we exhibit an n 2-set S whose arithmetic and geometric means constitute upper and lower bounds for per(F)/n!. We offer sharpened versions of these bounds when F has zero-valued entries.