strictly sub row hadamard majorization

‎let $textbf{m}_{m,n}$ be the set of all $m$by$n$ real matrices‎. ‎a matrix $r$ in $textbf{m}_{m,n}$ with nonnegative entries is called strictly sub row stochastic if the sum of entries on every row of $r$ is less than 1‎. ‎for $a,bintextbf{m}_{m,n}$‎, ‎we say that $a$ is strictly sub row hadamard majorized by $b$ (denoted by $aprec_{sh}b)$ if there exists an $m$by$n$ strictly sub row stochastic matrix $r$ such that $a=rcirc b$ where $x circ y$ is the hadamard product (entrywise product) of matrices $x,yintextbf{m}_{m,n}$‎. ‎in this paper‎, ‎we introduce the concept of strictly sub row hadamard majorization as a relation on $textbf{m}_{m,n}$‎. ‎also‎, ‎we find the structure of all linear operators $t:textbf{m}_{m,n} rightarrow textbf{m}_{m,n}$ which are preservers (resp‎. ‎strong preservers) of strictly sub row hadamard majorization‎.