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.