Fixed Points for Mean Non-expansive Mappings  

作　　者：Chun-xue Wu Li-juan Zhang 

机构地区：[1]Department of Mathematics, Yantai University, Yantai 264005, China

出　　处：《Acta Mathematicae Applicatae Sinica》2007年第3期489-494,共6页应用数学学报（英文版）

基　　金：the National Natural Science Foundation of China(No.10461006);the Natural Science Foundation of Shandong Province(Y002A10);the Younger Foundation of Yantai University(SX05Z9)

摘　　要：For a Banach Space X Garcia-Falset introduced the coefficient R（X） and showed that if R（X） 〈 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that ｜｜Tx - TY｜｜ ≤ a｜｜x - y｜｜ ＋ b｜｜x - Ty｜｜ for any x,y E X, where a,b ≥ 0, a ＋ b ≤ 1. We show that if R（X） 〈 1/1＋b then T has a fixed point in X.For a Banach Space X Garcia-Falset introduced the coefficient R（X） and showed that if R（X） 〈 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that ｜｜Tx - TY｜｜ ≤ a｜｜x - y｜｜ ＋ b｜｜x - Ty｜｜ for any x,y E X, where a,b ≥ 0, a ＋ b ≤ 1. We show that if R（X） 〈 1/1＋b then T has a fixed point in X.

关 键 词：Fixed point property mean non-expansive mapping normal structure 

分 类 号：O186.1[理学—数学]