Generalized fractional integral inequalities by means of quasiconvexity. (English) Zbl 1459.26037
Summary: Using the newly introduced fractional integral operators in [R. P. Agarwal et al., Fasc. Math. 56, 5–27 (2016; Zbl 1352.26003)] and [R. K. Raina, EAMJ, East Asian Math. J. 21, No. 2, 191–203 (2005; Zbl 1101.33016)], we establish some novel inequalities of the Hermite-Hadamard type for functions whose second derivatives in absolute value are \(\eta\)-quasiconvex. Results obtained herein give a broader generalization to some existing results in the literature by choosing appropriate values of the parameters under consideration. We apply our results to some special means such as the arithmetic, geometric, harmonic, logarithmic, generalized logarithmic, and identric means to obtain more results in this direction.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26A51 | Convexity of real functions in one variable, generalizations |
| 26A33 | Fractional derivatives and integrals |
Keywords:
Hermite-Hadamard inequality; convex functions; quasiconvex functions; special means; Riemann-Liouville fractional integral operatorsReferences:
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