A uinivariate extension of Jensens inequality

An Extension of Chebyshevs Inequality and Its Connection with Jensens Inequality

The aim of this paper is to show that Jensen’s Inequality and an extension of Chebyshev’s Inequality complement one another, so that they both can be formulated in a pairing form, including a second inequality, that provides an estimate for the classical one. 1. Introduction The well known fact that the derivative and the integral are inverse each other has a lot of interesting consequences, on...

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...

A Univariate Extension of Jensen's Inequality

The result in this paper exp lains some of the qualitative nature of Jensen's inequality. It is shown that the more disperse the distribution of a random variable is, the smaller is the expectation of any concave function of it. This result can be used to show the inadequacy of some current methods of reporting environmental data by using geometric means, and it extends the resu lt of I. Billic...

An extension of Maclaurins inequality

Let G be a graph of order n and clique number !: For every x = (x1; : : : ; xn) 2 Rn and 1 s !; set fs (G;x) = X fxi1 : : : xis : fi1; : : : ; isg is an s-clique of Gg ; and let s (G;x) = fs (G;x) ! s 1 : We show that if x 0; then 1 (G;x) 1=2 2 (G;x) 1=! ! (G;x) : This extends the inequality of Maclaurin (G = Kn) and generalizes the inequality of Motzkin and Straus. In addition, if x > 0; for e...