In this paper we derive several improved forms of the Jensen inequality, giving the necessary and sufficient conditions for them to hold in the case of the real Stieltjes measure not necessarily positive.The obtained relations are characterized via the Green function. As an application, our main results are employed for constructing some classes of exponentially convex functions and some Cauchy-type means.
Jensen inequality, Green function, refinement, convex function, exponentially convex function, Cauchy-type mean
KRNIC, MARIO; PECARIC, JOSIP; and RODIC, MIRNA
"More accurate Jensen-type inequalities for signed measures characterized via Green function and applications,"
Turkish Journal of Mathematics: Vol. 41:
6, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss6/11