Fractional exponentially \(m\)-convex functions and inequalities. (English) Zbl 1438.26089
Summary: In this article, we introduce a new class of convex functions involving \(m \in [0, 1]\), which is called exponentially \(m\)-convex function. Some new Hermite-Hadamard inequalities for exponentially \(m\)-convex functions via Reimann-Liouville fractional integral are deduced. Several special cases are discussed. Results proved in this paper may stimulate further research in different areas of pure and applied sciences.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
Keywords:
convex function; exponential convex function; Riemann-Liouville fractional integral inequalit; Hölder inequality; power-mean inequalityReferences:
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