On Levinson's inequality involving averages of 3-convex functions

By using the Levinson inequality we give the extension for 3-convex functions of Wulbert's result from Favard's Inequality on Average Values of Convex Functions, Math. Comput. Model. 37 (2003), 1383{1391. Also, we obtain inequalities with divided differences, and as a consequence, the convexity of higher order for function defined by divided difference is proved. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking at linear functionals associated with these new inequalities.

Some mappings related to Levinson’s inequality for Hilbert space operators

We observe properties of some mappings related to the Davis-Choi-Jensen inequality for Hilbert space operators. Using these results, we observe properties of some mappings related to Levinson?s operator inequality. Consequently, we obtain several refinements for each of these inequalities.

The generalised Hadamard inequality, g-convexity and functional Stolarsky means

We explore the role of weighted functional Stolarsky means in providing bounds in generalised Hadamard-type inequalities for g-convex functions. Refinements are given for Levinson's inequality and the generalised Hadamard inequality. Applications are made to multivariate weighted functional Stolarsky means.