On inequalities of periodic functions and their derivatives

Author:
Z. Ditzian

Journal:
Proc. Amer. Math. Soc. **87** (1983), 463-466

MSC:
Primary 26D10

DOI:
https://doi.org/10.1090/S0002-9939-1983-0684640-0

MathSciNet review:
684640

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The inequality is proved for many spaces of periodic functions. An analogue for sequences is also given.

**[1]**E. F. Beckenbach and R. Bellman,*Inequalities*, Springer-Verlag, Berlin and New York, 1961. MR**0158038 (28:1266)****[2]**R. Bellman,*A note on periodic functions and their derivatives*, J. London Math. Soc.**18**(1943). 140-142. MR**0009965 (5:230a)****[3]**Z. Ditzian,*Some remarks on inequalities of Landau and Kolmogorov*, Aequationes Math.**12**(1975), 145-51. MR**0380503 (52:1403)****[4]**K. Fan, O. Taussky and J. Todd,*Discrete analogues of inequalities by Wirtinger*, Monatsh. Math. Physik**59**(1955), 73-90. MR**0070676 (17:19b)****[5]**A. Kolmogorov,*On inequalities between upper bounds of the successive derivatives of an arbitrary function on an infinite interval*, Amer. Math. Soc. Transl. no. 4 (1949) (Russian original 1939). MR**0031009 (11:86d)****[6]**D. G. Northcott,*Some inequalities between periodic functions and their derivatives*, J. London Math. Soc.**14**(1939), 198-202. MR**0000417 (1:71c)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
26D10

Retrieve articles in all journals with MSC: 26D10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0684640-0

Article copyright:
© Copyright 1983
American Mathematical Society