On fractional biparameterized Newton-type inequalities

Abstract

Abstract In this work, we present a novel biparameterized identity that yields a family of one-, two-, three-, and four-point Newton-type formulas. Subsequently, we establish some new Newton-type inequalities for functions whose first derivatives are α-convex. The investigation is concluded with numerical examples accompanied by graphical representations to substantiate the accuracy of the obtained results.

Keywords

• Newton-type inequalities
• α-convex functions
• Riemann–Liouville operators
• Biparameterized identity
• Hölder and power mean inequalities