New Bounds for Parametrized Fractional Bullen Type Inequalities Pertaining Differentiable Functions

Abstract

In this thesis, the author formulated a new auxiliary result of Bullen type for a twice differentiable functions in terms of fractional integration operators. Based on this new identity, some generalized Bullen-type inequalities are obtained by employing convexity properties. Concrete examples are given to illustrate the results and correctness is sponsored by graphical analysis. Analysis is provided on estimations of bounds. According to calculations, improved H¨older and power mean inequalities give better upper bound results than classical inequalities. Applications to the quadrature rules, Modified Bessel functions and digamma functions are provided as well.