Let $A=(a_{n,k})_{n,k\geq 1}$ be a non-negative matrix. Denote by $L_{v,p,q,F}(A)$ the supremum of those $L$ that satisfy the inequality $$ \|Ax\|_{v,q,F} \ge L\| x\|_{v,p,F}, $$ where $x\geq 0$ and $x\in l_p(v,F)$ and also $v=(v_n)_{n=1}^\infty $ is an increasing, non-negative sequence of real numbers. If $p=q$, we use $L_{v,p,F}(A)$ instead of $L_{v,p,p,F}(A)$. In this paper we obtain a Hardy type formula for $L_{v,p,q,F}(H_\mu )$, where $H_\mu $ is a Hausdorff matrix and $0<q\leq p\leq 1$. Another purpose of this paper is to establish a lower bound for $\|A_{W}^{NM} \|_{v,p,F}$, where $A_{W}^{NM}$ is the Nörlund matrix associated with the sequence $W=\{w_n\}_{n=1}^\infty $ and $1<p<\infty $. Our results generalize some works of Bennett, Jameson and present authors.
In this paper we consider some matrix operators on block weighted sequence spaces $l_p(w,F)$. The problem is to find the lower bound of some matrix operators such as Hausdorff and Hilbert matrices on $l_p(w,F)$. This study is an extension of papers by G. Bennett, G.J.O. Jameson and R. Lashkaripour.
Max-min algebra and its various aspects have been intensively studied by many authors \cite{Baccelli,Green79} because of its applicability to various areas, such as fuzzy system, knowledge management and others. Binary operations of addition and multiplication of real numbers used in classical linear algebra are replaced in max-min algebra by operations of maximum and minimum. We consider two-sided systems of max-min linear equations
\begin{math}\emph{A}\otimes\emph{x}= B\otimes\emph{x}\end{math}, with given coefficient matrices \emph{A} and \emph{B}. We present a polynomial method for finding maximal solutions to such systems, and also when only solutions with prescribed lower and upper bounds are sought.