Search: authors:"Josip E. Pečarić"

Weighted averages of n-convex functions via extension of Montgomery’s identity

Using an extension of Montgomery’s identity and the Green’s function, we obtain new identities and related inequalities for weighted averages of n-convex functions, i.e. the sum \(\sum _{i=1}^m \rho _i h(\lambda _i)\) and the integral \(\int ^{b}_{a} \rho (\lambda ) h(\gamma (\lambda ))d\lambda \) where h is an n-convex function.

Weighted majorization inequalities for n-convex functions via extension of Montgomery identity using Green function

Weighted majorization theorems via generalization of Taylor’s formula

A new generalization of the weighted majorization theorem for n-convex functions is given, by using a generalization of Taylor’s formula. Bounds for the remainders in new majorization identities are given by using the Čebyšev type inequalities. Mean value theorems and n-exponential convexity are discussed for functionals related to the new majorization identities. MSC: 26D15, 26D20.

A Grüss-type inequality and its applications

We give a Grüss-type inequality which is a refinement of a result due to Dragomir and Agarwal. We also give its applications for the moments of random variables, guessing mappings, and Ozeki's inequality.