An Extension of the Erdös-debrunner Inequality to General Power Means

A Proof of Two Conjectures Related to the Erdös-debrunner Inequality

In this paper we prove some results which imply two conjectures proposed by Janous on an extension to the p-th power-mean of the Erdös–Debrunner inequality relating the areas of the four sub-triangles formed by connecting three arbitrary points on the sides of a given triangle.

On the Extension of the Erdös–mordell Type Inequalities

We discuss the extension of inequality RA c a rb + b a rc to the plane of triangle ABC . Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdös-Mordell inequality, and some inequalities of Erdös-Mordell type. Mathematics subject classification (2010): 51M16, 51M04, 14H50.

General Hardy-Type Inequalities with Non-conjugate Exponents

We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...

An Operator Extension of Bohr's inequality

Extension of Hardy Inequality on Weighted Sequence Spaces

Let and be a sequence with non-negative entries. If , denote by the infimum of those satisfying the following inequality: whenever . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). We considered this problem for certain matrix operators such as Norlund, Weighted mean, Ceasaro and Copson ma...