Abstract
Trapezoidal inequalities for functions of diverse natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via differentiable function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities 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 and new error estimates for the trapezoidal formula are provided as well. The ideas and techniques of this paper may stimulate further research.
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