‎in this paper, we study some kinds of majorizations on $textbf{m}_{n}$ and their linear or strong linear preservers. also, we find the structure of linear or strong linear preservers which are multiplicative, i.e.  linear or strong linear preservers like $phi $ with the property $phi (ab)=phi (a)phi (b)$ for every $a,bin textbf{m}_{n}$.

‎In this paper, we study some kinds of majorizations on $textbf{M}_{n}$ and their linear or strong linear preservers. Also, we find the structure of linear or strong linear preservers which are multiplicative, i.e.  linear or strong linear preservers like $Phi $ with the property $Phi (AB)=Phi (A)Phi (B)$ for every $A,Bin textbf{M}_{n}$.

In this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $Phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. The results generalise the results of several authors in literature including Xiang [Chang He Xiang, Fixed point theorem for generalized $Phi$-pseudocontra...

in this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. the results generalise the results of several authors in literature including xiang [chang he xiang, fixed point theorem for generalized $phi$-pseudocontra...

in the 1960's noboru iwahori and hideya matsumoto, eiichi abe and kazuo suzuki, and michael stein discovered that chevalley groups $g=g(phi,r)$ over a semilocal ring admit remarkable gauss decomposition $g=tuu^-u$, where $t=t(phi,r)$ is a split maximal torus, whereas $u=u(phi,r)$ and $u^-=u^-(phi,r)$ are unipotent radicals of two opposite borel subgroups $b=b(phi,r)$ and $b^-=b^-(phi,r)$ contai...

The pseudo-Brewster angle phi(pB) of minimum reflectance for p-polarized light and the principal angle phi at which incident linearly polarized light of the proper azimuth is reflected circularly polarized are considered as functions of the complex relative dielectric function epsilon of a dielectric-conductor interface over the entire complex epsilon plane. In particular, the spread of phi for...