有限簇多值Φ-拟伪压缩型映射公共不动点的迭代程序

Iteration process for common fixed points of a finite family of multi-valued Φ-quasi-pseudocontractive type mappings.

引入具误差的修正Mann和Ishikawa迭代程序及多值Φ-拟伪压缩型映射,在一致光滑实Banach空间证明了此迭代序列强收敛于具广义Lipschitzian连续的(一般未必连续或有界)多值Φ-拟伪压缩型映射有限簇的唯一公共不动点,统一和发展了包括王林和王刚(2006年)、周海云(2006年)、HUANG(2002年)、曾六川(2005年)、徐裕光(2004年)、张石生(2000年)和倪仁兴(2001和2002年)等近期许多相关结果.

Modified Mann and Ishikawa iterative processes with errors are introduced for a finite family of multi-valued Φ-quasi-pseudocontractive type mapping,and strong convergences of the iterative sequence to the unique common fixed point for a finite family of generalized Lipschitzian continuous（In general,it may not be continuous or may not be bounded.） multi-valued Φ-quasi-pseudocontractive type mappings are proved in uniformly smooth real Banach spaces.The results presented in this paper unify and improve some recent achievements by WANG Lin and WANG Gang（2006）,ZHOU Hai-yun（2006）,HUANG（2002）,ZENG Lu-chuan（2005）,XU Yu-guang（2004）,ZHANG Shi-sheng（2002）,NI Ren-xing（2001 and 2002） and others.