On properties of weighted Hardy constant for means
نویسندگان
چکیده
For a given weighted mean $\mathscr{M}$ defined on subinterval of $\mathbb{R}_+$ and sequence weights $\lambda=(\lambda_n)_{n=1}^\infty$ we define Hardy constant $\mathscr H(\lambda)$ as the smallest extended real number such that $$ \sum_{n=1}^\infty \lambda_n \mathscr{M}\big((x_1,\dots,x_n),(\lambda_1,\dots,\lambda_n)\big) \le \mathscr H(\lambda) \cdot x_n \text{ for all }x \in \ell^1(\lambda).$$ The aim this note is to present comprehensive study mapping H$. example prove it lower semicontinuous in pointwise topology. Moreover show whenever monotone Jensen-concave which continuous its then H$ with respect partitioning vector. Finally deliver some sufficient conditions $\lambda$ validate equality H(\lambda)=\sup every symmetric mean.
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2022
ISSN: ['1331-4343', '1848-9966']
DOI: https://doi.org/10.7153/mia-2022-25-65