Abstract For X, Y ∈ M n,m , it is said that X g-tridiagonal majorized by (and denoted ≺ gt ) if there exists a tridiagonal g-doubly stochastic matrix A such = AY . In this paper, the linear preservers and strong of are characterized on

In this paper, we shall prove three equilibrium existence theorems for generalized games in Hausdorff topological vector spaces.

Ky Fan’s result states that the real parts of the eigenvalues of an n × n complex matrix x are majorized by the eigenvalues of the Hermitian part of x. The converse was established by Amir-Moéz and Horn, and Mirsky, independently. We generalize the results in the context of complex semisimple Lie algebra. The real case is also discussed.

‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addi...

2 Let H = [ M K K∗ N ] be a Hermitian matrix. It is known that the eigenvalues of M ⊕N are 3 majorized by the eigenvalues of H . If, in addition, H is positive semidefinite and the block K 4 is Hermitian, then the following reverse majorization inequality holds for the eigenvalues: 5

in this paper, some results of singh, gopalakrishna and kulkarni (1970s) have been extended to higher order derivatives. it has been shown that, if $sumlimits_{a}theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $t(r, f)sim t(r, f^{(k)}), rrightarrowinfty$ if $theta(infty, f)=1$ and $t(r, f)sim (k+1)t(r, f^{(k)}), rrightarrowinfty$ if $th...