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3 results on '"Extremum values"'

2. Applications of Weighted Arithmetic-Geometric Means Inequality to Functional Inequalities

Author

Halil İbrahim Çelik

Subjects
Discrete mathematics, Matematik, Young's inequality, Inequality, media_common.quotation_subject, Young inequality, Functional inequalities, Elementary functions, Monotone sequences, Extremum values, Arithmetic-geometric means inequality,Young inequality,Extremum values,Functional inequalities,Elementary functions,Monotone sequences, lcsh:TA1-2040, Arithmetic-geometric means inequality, Elementary function, Geometric mean, lcsh:Engineering (General). Civil engineering (General), lcsh:Science (General), Mathematics, lcsh:Q1-390, Real number, media_common
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.

Published
2017
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3. The Extreme Points of the Set of Decreasing Failure Rate Distributions.

Author

FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS, Langberg ,Naftali A, Leon ,Ramon V, Lynch ,James, Proschan,Frank, FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS, Langberg ,Naftali A, Leon ,Ramon V, Lynch ,James, and Proschan,Frank

Abstract

Since the class of extended decreasing failure rate (EDFR) life distributions (i.e., distributions with support in (0, infinity)) is compact and convex, it follows from Choquet's Theorem that every EDFR life distribution can be represented as a mixture of extreme points of the EDFR class. We identify the extreme points of this class and of the standard class of decreasing failure rate (DFR) life distributions. Further, we show that even though the convex class of DFR life distributions is not compact, every DFR life distribution can be represented as a mixture of extreme points of the DFR class. (Author), Supersedes report dated Nov 78, AD-A064 786.

Published
1979

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