Simpson’s Integral Inequalities for Twice Differentiable Convex Functions

Abstract

Integral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In the present research article, we obtain new inequalities of Simpson’s integral type based on the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>φ</mml:mi></mml:math>-convex and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>φ</mml:mi></mml:math>-quasiconvex functions in the second derivative sense. In the last sections, some applications on special functions are provided and shown via two figures to demonstrate the explanation of the readers.