The necessary and sufficient condition for beamforming optimality for multiple-input multiple output (MIMO) systems with mean feedback has been derived and thoroughly investigated in this article. The condition is an inequality that contains parameters of the number of antennas, transmission power, and the singular values of channel mean matrix. When the beamforming optimality condition is sati...

Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in On the similarity of the entropy power inequality and the BrunnMinkowski inequality (IEEE Trans. Inform. Theory 30 (1984), no. 6, 837-839) the 1 n -concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We inve...

In this work, we investigate the tensor inequalities in t-product formalism. The involving power are proved to hold similarly as standard matrix scenarios. We then focus on norm inequalities. well-known arithmetic-geometric mean inequality, Hölder and Minkowski inequality generalized tensors. Furthermore, obtain some t-eigenvalue

In this paper, we prove an identity for differentiable convex functions related to conformable fractional integrals. Moreover, some parameterized inequalities are established by using To be more precise, obtained taking advantage of the convexity, Hölder inequality, and power mean inequality. Furthermore, previous new results presented special cases theorems.

In this paper we consider non-commutative analogue for the arithmeticgeometric mean inequality ab + (r − 1)b ≥ ra for two positive numbers a, b and r > 1. We show that under some assumptions the non-commutative analogue for ab which satisfies this inequality is unique and equal to r-mean. The case 0 < r < 1 is also considered. In particular, we give a new characterization of the geometric mean.

We discuss the exponential stability in mean square of mild solution for neutral stochastic partial functional differential equations with impulses. By applying impulsive Gronwall-Bellman inequality, the stochastic analytic techniques, the fractional power of operator, and semigroup theory, we obtain some completely new sufficient conditions ensuring the exponential stability in mean square of ...

The theory of means and their inequalities is fundamental to many fields including mathematics, statistics, physics, and economics.This is certainly true in the area of probability and statistics. There are large amounts of work available in the literature. For example, some useful results have been given by Shaked and Tong 1 , Shaked and Shanthikumar 2 , Shaked et al. 3 , and Tong 4, 5 . Motiv...