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Let $K$ denote a locally compact commutative hypergroup, $L^1(K)$ the hypergroup algebra, and $alpha$ a real-valued hermitian character of $K$. We show that $K$ is $alpha$-amenable if and only if $L^1(K)$ is $alpha$-left amenable. We also consider the $alpha$-amenability of hypergroup joins and polynomial hypergroups in several variables as well as a single variable.
Let $UC(K)$ denote the Banach space of all bounded uniformly continuous functions on a hypergroup $K$. The main results of this article concern on the $alpha$-amenability of $UC(K)$ and quotients and products of hypergroups. It is also shown that a S
This paper deals with the inequalities devoted to the comparison between the norm of a function on a compact hypergroup and the norm of its Fourier coefficients. We prove the classical Paley inequality in the setting of compact hypergroups which furt
Weighted group algebras have been studied extensively in Abstract Harmonic Analysis where complete characterizations have been found for some important properties of weighted group algebras, namely amenability and Arens regularity. One of the general
We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular we show that, a large class of commutative hypergroups are weakly amenable with the Cowling-Haager
Let $K$ be a commutative hypergroup and $alphain hat{K}$. We show that $K$ is $alpha$-amenable with the unique $alpha$-mean $m_alpha$ if and only if $m_alphain L^1(K)cap L^2(K)$ and $alpha$ is isolated in $hat{K}$. In contrast to the case of amenable