Generalizations and applications of Young’s integral inequality by higher order derivatives

Abstract

Abstract In the paper, the authors 1.generalize Young’s integral inequality via Taylor’s theorems in terms of higher order derivatives and their norms, and2.apply newly-established integral inequalities to estimate several concrete definite integrals, including a definite integral of a function which plays an indispensable role in differential geometry and has a connection with the Lah numbers in combinatorics, the exponential integral, and the logarithmic integral.

Keywords

• Young’s integral inequality
• Inverse function
• Taylor’s theorem
• Higher order derivative
• Lebesgue measure
• Norm