Banach空间中可数算子族的不动点集和广义混合均衡问题的公共解的强收敛性  

Strong convergence of common solutions of the fixed point sets of countable operators family and the generalized mixed equilibrium problems in Banach Spaces

作　　者：倪仁兴[1] 徐亚军 NI Ren-xing;XU Ya-jun(Department of Mathematical,Shaoxing University,Shaoxing 312000,China)

机构地区：[1]绍兴文理学院数学系,浙江绍兴312000

出　　处：《高校应用数学学报（A辑）》2024年第1期73-88,共16页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12171435)。

摘　　要：在自反Banach空间框架中,提出一类新的收缩投影算法,来逼近一闭Bregman拟渐近非扩张可数算子族的不动点集和广义混合均衡问题的公共解,建立了一闭Bregman拟渐近非扩张可数算子族的不动点集和广义混合均衡问题的公共解的强收敛性结果,并用一数值例子来支撑文中所得的结果.无论算子族从有限个到可数个,还是算子从Bregman相对非扩张到Bregman拟渐近非扩张等方面,均对Jantakarn K和Kaewcharoen A(2021)的结果进行了的拓展和补充.In the framework of reflexive Banach space,a new shrinking projection algorithm is proposed to approximate the common solutions of the solution of the generalized mixed equilibrium problems and thefixed point sets of a closed Bregman quasi-asymptotically nonexpansive countable operators family,and the strong convergence results of the common solutions of the solution of the gen-eralized mixed equilibrium problems and thefixed point sets of a closed Bregman quasi-asymptotically nonexpansive countable operators family are established.A numerical example of the iterative algo-rithm supporting our main results is presented.The results of Jantakarn K&Kaewcharoen A(2021)are extended and supplemented,whether the operator family is fromfinite to countable,or from Bregman relatively nonexpansive to Bregman quasi-asymptotically nonexpansive.

关 键 词：广义混合均衡问题 Bregman相对非扩张映像 Bregman拟渐进非扩张映射 收缩投影法 强收敛性 

分 类 号：O177.91[理学—数学]