Hermite-Hadamard type inequalities for \(F\)-convex function involving fractional integrals. (English) Zbl 1498.26063
Summary: In this study, the family \(F\) and \(F\)-convex function are given with its properties. In view of this, we establish some new inequalities of Hermite-Hadamard type for differentiable function. Moreover, we establish some trapezoid type inequalities for functions whose second derivatives in absolute values are \(F\)-convex. We also show that through the notion of \(F\)-convex we can find some new Hermite-Hadamard type and trapezoid type inequalities for the Riemann-Liouville fractional integrals and classical integrals.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26A51 | Convexity of real functions in one variable, generalizations |
| 26A33 | Fractional derivatives and integrals |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 34A08 | Fractional ordinary differential equations |
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