From the Ingham–Jessen property to mixed-mean inequalities
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.124999
Abstract: For every symmetric mean $\mathscr{M} \colon \bigcup_{n=1}^\infty I^n \to I$ (where $I$ an interval) and a nonzero function $W \colon \{1,\dots,n\} \to \mathbb{N} \cup \{0\}$, define an $n$-variable mean by $$\mathscr{M}_W(x):=\mathscr{M}\big(\underbrace{x_1,\dots,x_1}_{W(1)\text{-times}},\dots,\underbrace{x_n,\dots,x_n}_{W(n)\text{-times}}\big) \text{ for }x=(x_1,\dots,x_n) \in… read more here.
Keywords: mixed mean; mathscr big; big mathscr; ingham jessen ... See more keywords
Some refinements of operator reverse AM-GM mean inequalities
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-017-1557-y
Abstract: AbstractIn this paper, we prove the operator inequalities as follows: Let A,B$A,B$ be positive operators on a Hilbert space with 0 read more here.
Keywords: operator reverse; mean inequalities; frac; refinements operator ... See more keywords
An interpolation of Jensen's inequality and its converses with applications to quasi-arithmetic mean inequalities
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Inequalities"
DOI: 10.7153/jmi-2019-13-08
Abstract: In this paper, we show an interpolation of Davis-Choi-Jensen operator inequality and the converse inequality for Hilbert space operators. As applications, we obtain an interpolation of quasi-arithmetic mean inequalities and the converse inequalities. read more here.
Keywords: inequality; inequalities interpolation; mean inequalities; arithmetic mean ... See more keywords