Fractional trapezium-like inequalities involving generalized relative semi-\(( m, h_1 , h_2)\)-preinvex mappings on an \(m\)-invex set. (English) Zbl 1467.26015
Ukr. Math. J. 72, No. 12, 1886-1906 (2021) and Ukr. Mat. Zh. 72, No. 12, 1633-1650 (2021).
Summary: We deduce a fractional integral equality for twice differentiable mappings defined on an \(m\)-invex set. By using this equality, we obtain new estimates generalizing trapezium-like inequalities for mappings whose second-order derivatives are generalized relative semi-\(( m, h_1 ,h_2)\)-preinvex via fractional integrals. We also discuss some new special cases that can be deduced from our main results.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26A33 | Fractional derivatives and integrals |
| 26A51 | Convexity of real functions in one variable, generalizations |
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