About the Common Fixed Point Problem of Mean Nonexpanded Mapping
Yan Jun Wu · Journal of Yantai University · 2004
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 T_1 and T_2 are both mean nonexpanded mappings and they satisfy T_1T_2=T_2T_1,then T_1T_2 has one and only one fixed point in K.Furthermore,T_1 and T_2 have one and only one common fixed point in K.