A unified approach to several inequalities involving functions and derivatives
Czechoslovak Mathematical Journal (2001)
- Volume: 51, Issue: 2, page 363-376
- ISSN: 0011-4642
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topDuoandikoetxea, Javier. "A unified approach to several inequalities involving functions and derivatives." Czechoslovak Mathematical Journal 51.2 (2001): 363-376. <http://eudml.org/doc/30640>.
@article{Duoandikoetxea2001,
abstract = {There are many inequalities measuring the deviation of the average of a function over an interval from a linear combination of values of the function and some of its derivatives. A general setting is given from which the desired inequalities are obtained using Hölder’s inequality. Moreover, sharpness of the constants is usually easy to prove by studying the equality cases of Hölder’s inequality. Comparison of averages, extension to weighted integrals and $n$-dimensional results are also given.},
author = {Duoandikoetxea, Javier},
journal = {Czechoslovak Mathematical Journal},
keywords = {inequalities; averages of functions; quadrature; inequalities; averages of functions; quadrature; weighted integrals},
language = {eng},
number = {2},
pages = {363-376},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A unified approach to several inequalities involving functions and derivatives},
url = {http://eudml.org/doc/30640},
volume = {51},
year = {2001},
}
TY - JOUR
AU - Duoandikoetxea, Javier
TI - A unified approach to several inequalities involving functions and derivatives
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 363
EP - 376
AB - There are many inequalities measuring the deviation of the average of a function over an interval from a linear combination of values of the function and some of its derivatives. A general setting is given from which the desired inequalities are obtained using Hölder’s inequality. Moreover, sharpness of the constants is usually easy to prove by studying the equality cases of Hölder’s inequality. Comparison of averages, extension to weighted integrals and $n$-dimensional results are also given.
LA - eng
KW - inequalities; averages of functions; quadrature; inequalities; averages of functions; quadrature; weighted integrals
UR - http://eudml.org/doc/30640
ER -
References
top- 10.1090/S0002-9939-1995-1283537-3, Proc. Amer. Math. Soc. 123 (1995), 3775–3781. (1995) Zbl0860.26009MR1283537DOI10.1090/S0002-9939-1995-1283537-3
- Methods of Numerical Integration, Academic Press, New York, 1975. (1975) MR0448814
- Bounds on the deviation of a function from its averages, Czechoslovak Math. J. 42 (1992), 289–310. (1992) Zbl0780.26011MR1179500
- Inequalities Involving Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991. (1991) MR1190927
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