New parameterized inequalities for twice differentiable functions

Abstract

The present paper first establishes that an identity involving generalizedfractional integrals is proved for twice differentiable functions by using aparameter. By using this equality, we obtain some parameterized inequalitiesfor the functions whose second derivatives in absolute value are convex.Finally, we show that our main results reduce to trapezoid, midpoint Simpsonand Bullen-type inequalities which are proved in earlier published papers.