摘要
先介绍全拟-φ-渐近非扩张映象的概念,然后在具有Kadec—Klee性质的一致光滑、严格凸的Banach空间的框架下,利用混合收缩投影的迭代算法,用以寻求广义混合平衡问题的解集GMEP,可数簇全拟-φ-渐近非扩张映象的不动点集(?)F(S_(i))和极大单调算子的零点集T^(-1)0的公共元.在适当的条件下,证明了逼近于这一公共元的强收敛定理.推广和改进了一些最新结果.
The purpose of this paper is first to introduce the concept of total quasi-φ-asympto- tically nonexpansive mapping and then consider a hybrid shrinking projection method for find- ing a common element of the set GMEP of solutions of a generalized mixed equilibrium problem, the set ∞∩i=1 F（Si） of common fixed points of a countable family of total quasi-φ-asymptotically nonexpansive mappings { Si}∞/i=1 and the set T-^1 O of zeros of a maximal mono- tone operator T in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. It is proven that under appropriate conditions, the sequence generated by the hybrid shrinking projection method, converges strongly to some point in GMEP ∩ ^T^-1 O ∩（ ∞∩i=1 F（Si））. This new result represents the improvement, complement and development of the previously known ones in the literature.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2014年第2期283-302,共20页
Acta Mathematica Scientia
基金
四川省科技厅项目(2012JYZ011)
教育厅重点项目(13ZA0199)
四川省教育厅资助科研项目(14ZA0271)资助
关键词
广义混合平衡问题
全拟-φ-渐近非扩张映象
拟-φ-渐近非扩张映象
拟-φ-非扩张映象
混合收缩投影
β-逆强单调映象
极大单调算子
Generalized mixed eqUlllDrlum proDlem
Total quasi-φ-asymptoticallynonexpansive mapping
Quasi--asymptotically nonexpansive mapping
Quasi-φ-nonexpansive mapping
Hybrid shrinking projection
β-Inverse strongly monotone mapping
Maximal monotone oper-ator.
