Mond, Integral inequilities of Hermite-Hadamard type for log-convex functions, Demonst.

Pachpatte, A note on integral inequalities involving two log-convex functions, Math.

M}]-curves for non-quasianalytic, strongly log-convex weight sequences M of moderate growth.

M)] such that M is strongly log-convex and has moderate growth admit a convenient setting, no matter if M is quasianalytic or not.

is log-convex in the Jensen sense on I, if and only if

It follows that a positive function is log-convex in the Jensen sense if and only if it is 2-exponentially convex in the Jensen sense.

Contributors here take the task on, with papers on such aspects as the maximal characterization of Hardy-Sobolev spaces on manifolds, approximately Gaussian marginals and the hyperplane conjecture, on the existence of sub-Gaussian directions for log-concave measures, isoperimetric bounds on convex manifolds, and the

log-convex density conjecture.

We note that 0-convex function is simply log-convex function and 1-convex function is ordinary convex function.

If r = 0 and p [not equal to] 0, then f is log-convex, it follows from (1) and (2) that

Niculescu, The Hermite-Hadamard inequality for

log-convex functions, Nonlinear Anal.

i[phi]] (v - u) = v - u, the [phi]-convex set K becomes the convex set and consequently, [phi]-convex, [phi]-invex, and log-[phi]-invex functions reduce to convex and

log-convex functions.

Keywords and Phrases: Ostrowski inequality, Gruss inequality, Cebysev inequality, Convex functions,

Log-convex functions.