中文摘要：

A_r~（λ_3）（λ_1,λ_2;E）一权函数是一类广义的权函数,可视为许多经典权函数的推广.文中给出了关于A_r~（λ_3）（λ_1,λ_2;E）-权的和与积的运算性质,并进而证明了A_r^（λ_3）（λ_1,λ_2;E）-权函数的两个充要条件.

英文摘要：

A_r~（λ_3）（λ_1,λ_2;E）- weight is a wide weight function,can also be seen as the generalization of many classic weight functions.In this paper,we first give properties of the addition and multipUcation for A_r~（λ_3）（λ_1,λ_2;E）- weight,and we also establish two necessary and sufficient conditions.