本文得到了赋β-范空间(0＜β■1)的单位球面(或球)上的等距映射可以延拓为全空间上的线性等距映射的一些充分条件,然后在赋β-范线性空间E中研究(λ,Ψ,2)-等距映射的延拓问题,主要结果为：正齐性映射V_0：B_1(E)→B_1(E)是(1,Ψ,2)-等距的充要条件为‖V_0x‖■‖x‖,■_x∈B_1(E),推广了Zhang L．的相应结果．

We first obtain some sufficient conditions for an isometric mapping defined on the unit sphere(or ball)of aβ-normed space(0＜β■1)can bc extended to be a linear isometry on the whole space.Secondly,in aβ-normed space E,we study the extension problem of(λ,Ψ,2)-isometry.The main result says that positively ho- mogeneous mapping V_0:B_1(E)→B_1(E)is(1,Ψ,2)-isometry if and only if‖V_0x‖■‖x‖,■x∈B_1(E),hence this result generalizes the corresponding result in Zhang L.