Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide  inequalities for functions that are, intuitively, "very" convex. These inequalities are simple to apply and can be used to generalize and extend previous results or to derive new results. We apply our inequalities to various applications from different fields, including risk aversion, risk measures, moment generating functions, and log-likelihood functions  .
Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These inequalities are simple to apply and can be used to generalize and extend previous results or to derive new results. We apply our inequalities to quantify the notion "more risk averse" provided in \mbox{%DIFAUXCMD pratt1978risk applications from different fields, including risk measures, moment generating functions, log-likelihood functions , and Hermite-Hadamard type inequalities .
A
Jensen-type
R
various
quantify the notion "more risk averse" provided in \mbox{%DIFAUXCMD pratt1978risk
D
aversion, risk
D
and
A
, and Hermite-Hadamard type inequalities