Inequalities related to Pólya matrices. (English) Zbl 0582.34012
General inequalities 4, Mem. E. F. Beckenbach, 4th Int. Conf., Oberwolfach/Ger. 1983, ISNM 71, 307-322 (1984).
[For the entire collection see Zbl 0573.00004.]
A Pólya matrix P is a 0-1-matrix representing a certain differential system. By means of a minimum principle, this system induces the class of P-concave functions for which we derive a variety of integral inequalities. The proofs are based on the total positivity properties of the extended Green’s kernel of the underlying differential system.
A Pólya matrix P is a 0-1-matrix representing a certain differential system. By means of a minimum principle, this system induces the class of P-concave functions for which we derive a variety of integral inequalities. The proofs are based on the total positivity properties of the extended Green’s kernel of the underlying differential system.
MSC:
| 34A40 | Differential inequalities involving functions of a single real variable |
