We formulate and prove a generalization of Hardy’s inequality [27] in terms random variables show that it contains the usual (or familiar) continuous discrete forms inequality. Next we improve recent version by Li Mao [42] with weights for general Borel measures mixed norms so implies Liao [43] Hardy Muckenhoupt [48] as well norm versions due to Littlewood [29], Bliss [8], Bradley [14]. An equi...

the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...