The fixed point property of mean non-expansive mapping
Wang Jun-ming · Journal of Natural Science of Heilongjiang University · 2006
[WT5BZ]Let T be a mapping from weak compact convex subset K of a Banach space X into itself satisfying the following inequality: ‖Tx-Ty‖≤a‖x-y‖+b‖x-Tx‖+c‖x-Ty‖,x,y∈K,a,b,c≥0,a+b+c≤1. The fixed point problem of the mapping T is discussed. It is concluded that if Garcia-Falset geometric coefficient R(X)21+2b+c, then the mapping T has the fixed point.