Hilbert空间中的平衡问题与渐近k-严格伪压缩映像的强收敛定理

Strong Convergence Theorems for Equilibrium Problem and Asymptotically k-Strictly Pseudocontractive Mapping In Hilbert Space

为了把不动点问题与平衡问题结合起来以寻找它们的公共解,在Hilbert空间中引入一种变形的Mann迭代程序,用以逼近两个集合的公共点,这两个集合分别是平衡问题的解集和渐近k-严格伪压缩映像的不动点集合,并在适当的条件下,利用混杂投影算法证明了一个关于平衡问题与渐近k-严格伪压缩映像的不动点问题的公共点的强收敛定理.

In this paper,the purpose is to combine the fixed points and equilibrium problem to find their common solutions.Therefore,an modification of Mann iterative program is introduced to find the common element of the set of solutions of equilibrium problem and the set of fixed points of asymptotically kstrictly pseudocontractive mapping in Hilbert space.And by using hybrid projection algorithms,a strong convergence theorem about their common points under the suitable conditions is proved.