Banach空间中均衡问题和弱相对非扩展映射的强收敛定理及其应用(英文)

Strong Convergence Theorems for Equilibrium Problems and Weakly Relatively Nonexpansive Mappings in Banach Spaces and their Applications

本文在Banach空间中设计了一些新的杂交迭代算法用以逼近一类均衡问题解集和弱相对非扩展映射不动点集或极大单调算子零点集的公共元.得到了一些强收敛的结论,并将它们推广到逼近一类均衡问题解集和有限个弱相对非扩展映射公共不动点集或有限个极大单调算子公共零点集的公共元的情形.最后,展示了本文的迭代算法在最优化问题上的应用.

In this paper,some new hybrid iterative schemes for approximating the common element of the set of solutions of an equilibrium problem and the set of fixed points of weakly relatively nonexpansive mappings or the set of zero points of maximal monotone operators in a Banach space are proposed.Some strong convergence theorems are proved and are also extended to the finite cases.Moreover,the applications of the newly obtained iterative schemes on optimization problems are demonstrated.