Some opial, Lyapunov, and De IaValée poussin inequalities with nonhomogeneous boundary conditions

Abstract

We derive Opial-type inequalities for a class of real functions satisfying nonhomogenous boundary conditions and determine the best constant and extremals. The results are then used to obtain generalized Lyapunov and De la Valée Poussin inequalities.

Keywords

• Opial inequality
• Lyapunov inequality
• De la Valée Poussin inequality
• Nonhomogeneous boundary conditions
• Best constants
• Extremals