Journal of Inequalities and Applications
Volume 5 (2000), Issue 1, Pages 11-37

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

Richard C. Brown,1 A. M. Fink,2 and Don B. Hinton3

1Department of Mathematics, University of Alabama, Tuscaloosa 35487-0350, AL, USA
2Department of Mathematics, Iowa State University, Ames 50011, IA, USA
3Department of Mathematics, University of Tennessee, Knoxville 37996, TN , USA

Received 18 January 1999; Revised 30 January 1999

Copyright © 2000 Richard C. Brown et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.