Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications

Abstract

Trapezoidal inequalities for functions of divers natures are useful in numericalcomputations. The authors have proved an identity for a generalized integraloperator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have beendiscovered. It is pointed out that the results of this research provide integralinequalities for almost all fractional integrals discovered in recent past decades.Various special cases have been identified. Some applications of presented results to special means have been analyzed. The ideas and techniques of thispaper may stimulate further research.