一类广义非扩张映射的不动点性质  

The Fixed Point Property of a Class of Generalized Non-expansive Mappings

作　　者：张少勇 朱鹏 ZHANG Shao-yong;ZHU Peng(School of Applied Science,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院

出　　处：《哈尔滨理工大学学报》2019年第5期145-148,共4页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11781181)

摘　　要：将W.kirk最著名的结果:具有正规结构自反的Banach空间关于非扩张映射具有不动点性质,推广到更加一般的映射形式,即:‖T(x)-T(y)‖≤a 1(t)(d(x,y))‖x-y‖+a 2(t)(d(x,y))‖x-T(x)‖+a 3(t)(d(x,y))‖x-T(y)‖,其中∑3 i=1 a i(t)≤1,且a i(t):(0,+∞)→(0,1)单调递减,研究了具有正规结构自反的Banach空间关于上述映射具有不动点性质。In this paper,the most famous result by W.kirk is that the non-expansive mapping has the fixed point property in a Banach space with normal structure reflexive is extended to a more general form of mapping,namely:‖T(x)-T(y)‖≤a 1(t)(d(x,y))‖x-y‖+a 2(t)(d(x,y))‖x-T(x)‖+a 3(t)(d(x,y))‖x-T(y)‖,where a i(t):(0,+∞)→(0,1)monotone decreases,a reflexive Banach space X with normal structure has the fixed point property for the mapping mentioned above.

关 键 词：广义非扩张映射 正规结构 自反性 不动点性质 

分 类 号：O177.3[理学—数学]