Abstract
In this paper, we introduce the notion of strongly \({\varphi_{h}}\) -convex functions with respect to c > 0 and present some properties and representation of such functions. We obtain a characterization of inner product spaces involving the notion of strongly \({\varphi_{h}}\) -convex functions. Finally, a version of Hermite–Hadamard-type inequalities for strongly \({\varphi_{h}}\) -convex functions is established.
Highlights
We introduce the notion of strongly φh-convex functions defined in normed spaces and present some properties of them
We start with the following lemma which gives some relationships between strongly φh-convex functions and φh-convex functions in the case where X is a real inner product space
The following example shows that the assumption that X is an inner product space is essential in the above lemma
Summary
We introduce the notion of strongly φh-convex functions defined in normed spaces and present some properties of them. A version of Hermite–Hadamard-type inequalities for strongly φh-convex functions is presented.
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