集值映象序列的公共不动点定理

Common Fixed Point Theorem for Set Valued Mapping Sequence

研究了度量空间集值映象的不动点问题，给出了如下结果：设Ｔｉ：Ｘ→Ｐｆ（Ｘ）（ｉ＝１，２，…）为集值映象序列，满足：存在０＜α＜１，对任意ｉ，ｊ∈Ｚ＋，ｘ，ｙ∈Ｘ，有δ（Ｔｉｘ，Ｔｊｙ）≤αｍａｘ｛ｄ（ｘ，ｙ），ｄ（ｘ，Ｔｉｘ），ｄ（ｙ，Ｔｊｙ），１２［ｄ（ｘ，Ｔｊｙ）＋ｄ（ｙ，Ｔｉｘ）］，ｄ（ｘ，Ｔｊｙ）ｄ（ｙ。

In present paper, the question of common fixed point for set valued mapping sequence is investigated and the following result is abtainted. Let T i:X→P f(X) (i=1,2,…) is set valued mapping sequence satisfies δ(T ix,T j y)≤α max {d(x,y),d(x,T i x),d(y,T j y)12[d(x,T jy)+d(y,T ix)],d(x,T j y)·d(y,T ix)} for some 0<α<1 and all x,y∈X, then {T i} have a fixed point u in X .