Parameterized inequalities based on three times differentiable functions

Abstract

Abstract This paper presents a general identity including two real parameters for three times differentiable functions. By using this equality, we prove several inequalities by using diverse function classes such as convex function, bounded function, Lipschitzian function, and function of bounded variation. By special choices of the parameters in the obtained results, we present some well-known inequalities: midpoint inequality, trapezoid inequality, Milne inequality, Bullen inequality, and Simpson inequality.

Keywords

• Convex function
• Hermite–Hadamard inequality
• Hölder inequality
• Bounded function
• Lipschitzian function
• Function of bounded variation