Some new parameterized Newton-type inequalities for differentiable functions via fractional integrals - Ali, Muhammad Aamir; Goodrich, Christopher S.; Budak, Hüseyin (Journal of inequalities and applications, 2023)
The main goal of the current study is to establish some new parameterized Newton-type inequalities for differentiable convex functions in the setting of fractional calculus. For this, first we prove a parameterized integral identity involving fractional integrals and then prove Newton-type inequalities for differentiable convex functions. It is also shown that the newly established parameterized inequalities are refinements of the already proved inequalities in the literature for different choices of parameters. Finally, we discuss a mathematical example along with a plot to show the validity of the newly established inequalities.