Abstract
References
- [1] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, 2nd. ed., Cambridge, New York 1959.
- [2] N. D. Kazarinoff, Analytic Inequalities, Holt, Rinehart and Winston, New York, 1961.
- [3] I. J. Maddox, Elements of Functional Analysis, Second ed., Cambridge Univ. Press, 1988.
- [4] Thomas.J. Mildford, Olympiad Inequalites, 2006, http://www.unl.edu/amc.
- [5] W. Rudin, Real and Complex Analysis , McGraw-Hill Book Company, New York, 1987.
Abstract
In this paper we prove the functional inequality $f(x)^{f(x)}\leq g(x)^{g(x)}$ for positive real functions $f$ and $g$ satisfying natural conditions and apply it to derive
inequalities between some of the elementary functions and to prove monotonocity of certain sequences of real numbers.
Keywords
Arithmetic-geometric means inequality Young inequality Extremum values Functional inequalities Elementary functions Monotone sequences
References
- [1] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, 2nd. ed., Cambridge, New York 1959.
- [2] N. D. Kazarinoff, Analytic Inequalities, Holt, Rinehart and Winston, New York, 1961.
- [3] I. J. Maddox, Elements of Functional Analysis, Second ed., Cambridge Univ. Press, 1988.
- [4] Thomas.J. Mildford, Olympiad Inequalites, 2006, http://www.unl.edu/amc.
- [5] W. Rudin, Real and Complex Analysis , McGraw-Hill Book Company, New York, 1987.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | April 30, 2017 |
| Published in Issue | Year 2017 Volume: 2 Issue: 1 |