Variations and Generalizations of Bohr′s Inequality

AbstractIn this paper we provide an account of various results that have been obtained concerning Bohr′s inequality with emphasis on several generalizations

Weighted Favard and Berwald Inequalities

AbstractWeighted versions of the Favard and Benwald inequalities are proved in the class of monotone and concave (convex) functions. Some necessary majorization estimates and a double-weight characterization for a Favard-type inequality are included

HERMITE INTERPOLATION WITH GREEN FUNCTIONS AND POSITIVITY OF GENERAL LINEAR INEQUALITIES FOR n-CONVEX FUNCTIONS

We state new general linear identities and inequalities involving n-convex functions using Hermite interpolation polynomials and Green functions. We also study positivity conditions of our stated inequalities. Moreover, we state related inequalities for n-convex functions at a point. Bounds for the reminders in new generalizations of general linear inequalities are given by using Cebysev functional, Ostrowski- and Gruss- types inequalities

On some inequalities of the Grüss-Barnes and Borell type

Some new generalizations of the Grüss-Barnes and Borell inequalities are proved. A new proof, using the classical Chebyshev inequality, for the case of two functions is presented and applied. A crucial inequality for $n$ functions by C. Borell \ref[J. Math. Anal. Appl. 41 (1973), 300--312; MR0315073 (47 \#3622)] is also discussed. Some recent results are sharpened and complemented. Interpolated or weighted versions of some of the inequalities are pointed out.Godkänd; 1994; 20070208 (kani)</p