Journal of Inequalities and Applications
Volume 3 (1999), Issue 2, Pages 183-214

On an inequality of Kolmogorov type for a second-order difference expression

A. Delil1 and W. D. Evans2

1Cuma Mahallesi, Uzay sokak No: 6, 45500-Soma, Manisa, Turkey
2School of Mathematics, University of Wales Cardiff, Senghennydd Road, Cardiff CF2 4 YH, UK

Received 30 April 1998; Revised 23 June 1998

Copyright © 1999 A. Delil and W. D. Evans. 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.


In this paper we discuss an inequality of Kolmogorov type for the square of a second-order formally symmetric difference expression in the limit point case. A connection between the existence of the inequality and the Hellinger–Nevanlinna m(λ) function associated with the difference expression is established and it is shown that the best constant in the inequality is determined by the behaviour of the m-function. Analytical and computational results are obtained for specific classes of problems. Also necessary and sufficient conditions for the powers of the difference expression to be partially separated are given.