On the refinements of the Hermite-Hadamard inequality
1 Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, 54600, Pakistan
2 Faculty of Textile Technology, University of Zagreb, Prilaz Baruna Filipovića 28A, 10000, Zegreb, Croatia
Journal of Inequalities and Applications 2012, 2012:155 doi:10.1186/1029-242X-2012-155Published: 5 July 2012
In this paper, we present some refinements of the classical Hermite-Hadamard integral inequality for convex functions. Further, we give the concept of n-exponential convexity and log-convexity of the functions associated with the linear functionals defined by these inequalities and prove monotonicity property of the generalized Cauchy means obtained via these functionals. Finally, we give several examples of the families of functions for which the results can be applied.