【摘要】 X表示Banach空间,K是X中的非空有界闭凸子集且具有正规结构,已知平均非扩张映射T:K→K,满足‖Tx-Ty‖≤a‖x-y‖+b‖x-Ty‖, x,y∈K,a,b≥0,a+b≤1在K中存在唯一的不动点.本文给出若T1和T2都是如上所定义的平均非扩张映射,且满足T1T2=T2T1,则T1T2在K中存在唯一的不动点,并且T1和T2在K中存在唯一的公共不动点.更多还原

【Abstract】 Let X be a Banach space,and K be a nonempty bounded closed convex subset of X which has a normal structure. Define a mean nonexpanded mapping T on K as:‖Tx-Ty‖≤a‖x-y‖+b‖x-Ty‖, for any x,y in K and any nonnegative real numbers a and b with a+b≤1. Then T has one and only one fixed point in K.If T₁ and T₂ are both mean nonexpanded mappings and they satisfy T₁T₂=T₂T₁,then T₁T₂ has one and only one fixed point in K.Furthermore,T₁ and T₂ have one and only one common fixed point in K.更多还原