TY  - JOUR
T1  - Applications of Weighted Arithmetic-Geometric Means Inequality to Functional Inequalities
AU  - Çelik, Halil İbrahim
PY  - 2017
DA  - April
DO  - 10.30931/jetas.303624
JF  - Journal of Engineering Technology and Applied Sciences
JO  - JETAS
PB  - Muhammet KURULAY
WT  - DergiPark
SN  - 2548-0391
SP  - 27
EP  - 31
VL  - 2
IS  - 1
LA  - en
AB  - 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 deriveinequalities between some of the elementary functions and to prove monotonocity of certain sequences of real numbers.
KW  - Arithmetic-geometric means inequality
KW  - Young inequality
KW  - Extremum values
KW  - Functional inequalities
KW  - Elementary functions
KW  - Monotone sequences
CR  - [1] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, 2nd. ed., Cambridge, New York 1959.
CR  - [2] N. D. Kazarinoff, Analytic Inequalities, Holt, Rinehart and Winston, New York, 1961.
CR  - [3] I. J. Maddox, Elements of Functional Analysis, Second ed., Cambridge Univ. Press, 1988.
CR  - [4] Thomas.J. Mildford, Olympiad Inequalites, 2006, http://www.unl.edu/amc.
CR  - [5] W. Rudin, Real and Complex Analysis , McGraw-Hill Book Company, New York, 1987.
UR  - https://doi.org/10.30931/jetas.303624
L1  - https://dergipark.org.tr/en/download/article-file/313113
ER  -