A Remark on the Kolmogorov–Stein Inequality

A Remark on the Mandl’s Inequality

So, we have (1.2) p1p2 · · · pn < (pn 2 )n (n ≥ 9), where also holds true by computation for 5 ≤ n ≤ 8. In other hand, one can get a trivial lower bound for that product using Euclid’s proof of infinity of primes; Letting En = p1p2 · · · pn−1 for every n ≥ 2, it is clear that pn < En. So, if pn < En < pn+1 then En should has a prime factor among p1, p2, · · · , pn which isn’t possible. Thus En ...

A remark on the slope inequality for fibred surfaces

We define a fibration, or fibred surface to be the data of a smooth projective surface X with a surjective morphism f to a smooth complete curve B. We also assume that f has connected fibres. Recall that such a morphism is automatically flat and proper, and that the general fibre of a fibration is smooth. The genus of the general fibre is called genus of the fibration. Define a (-1)-curve (resp...

Remark on Ozeki Inequality for Convex Polygons

This paper gives proof of a discrete inequality that represents Ozeki’s inequality for convex polygons and its converse. The proof is based on determining eigenvalues of one nearly tridiagonal symmetric matrix.

A Remark on Gwinner’s Existence Theorem on Variational Inequality Problem

Gwinner (1981) proved an existence theorem for a variational inequality problem involving an upper semicontinuous multifunction with compact convex values. The aim of this paper is to solve this problem for a multifunction with open inverse values.

A Remark on a Norm Inequality for Square Matrices