Banach空间中一类广义非扩张映像族公共不动点问题研究  

COMMON FIXED POINTS FOR A FAMILY OF GENERALIZED NONEXPANSIVE MAPPINGS IN BANACH SPACES

作　　者：马笳棋 周姝 彭丽辉 Ma Jiaqi;Zhou Shu;Peng Lihui(School of Statistics and Mathematics Zhejiang Gongshang University)

机构地区：[1]浙江工商大学统计与数学学院,杭州310018

出　　处：《高等学校计算数学学报》2023年第1期16-24,共9页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(编号11971431);浙江省一流学科A类(浙江工商大学统计学)资助。

摘　　要：1引言Banach空间中非扩张映像的不动点问题,由于其在变分不等式、优化及参数估计问题、反问题、图像恢复和信号处理等领域中的广泛应用[3,10,13-14],具有相当重要的理论意义和应用价值,一直是诸多学者的关注重点.不动点问题研究,包括不动点的存在判别、不动点集性质研究、不动点构造以及不动点理论在相关领域的应用等.In the present paper,we study the existence of the common fixed points for a family of generalized nonexpansive mappings in the framework of certain Banach spaces.We propose a new algorithm for common fixed points of a family of generalized nonexpansive mappings in Banach spaces and the strong convergence theorem of the proposed algorithm is presented.The results we get extend and improve the corresponding conclusion in [J Math Anal Appl,2003,279:372-379] and[J.Approx.Theory,2005,134:257-266] etc.Finally,the numerical experiments suggest that the new algorithm could be faster than the algorithm of [Chinese Annals of Mathematics,2010,31A(5):565-570].

关 键 词：BANACH空间 非扩张映像 公共不动点 不动点理论 变分不等式 参数估计问题 不动点集 不动点问题 

分 类 号：O177.91[理学—数学]