The strongly $(M,N)_h$-convex functions and Hadamard inequalities

Abstract

We define highly $(M,N)_h$-convex functions with respect to $\alpha> 0$ and discuss certain features. With the help of the idea of strongly $(M,N)_h$-convex functions, we are able to characterize inner product spaces (IPS). Finally, strongly $(M,N)_h$-convex functions are established to have Hadamard inequalities.