Integral inequalities of the Hermite – Hadamard type for $K$ -bounded norm convex mappings

Abstract

We obtain some inequalities of the Hermite – Hadamard type for $K$-bounded norm convex mappings between two normed spaces. The applications for twice differentiable functions in Banach spaces and functions defined by power series in Banach algebras are presented. Some discrete Jensen-type inequalities are also obtained.