In this paper, we establish new inequalities of the Hermite-Hadamard,
midpoint and trapezoid types for functions whose first derivatives in
absolute value are ?-quasiconvex by means of generalized fractional integral
operators with respect to another function ? : [?,?] ? (0,?). Our theorems
reduce to results involving the Riemann-Liouville fractional integral
operators if ? is the identity map, and results involving the Hadamard
operators if ?(x) = ln x. More inequalities can be deduced by choosing
different bifunctions for ?. To the best of our knowledge, the results
obtained herein are new and we hope that they will stimulate further
interest in this direction.
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