q-一致光滑和严格凸的Banach空间中的无穷个严格伪压缩映射的混合迭代算法

A General Composite Iterative Algorithm for an Infinite Family of Strictly Pseudo-Contractive Mappings in q-Uniformly Smooth and Strictly Convex Banach Spaces

在q-一致光滑和严格凸的Banach空间中,研究了无穷个严格伪压缩映射的混合迭代算法,证明了由这种新的算法产生的序列强收敛于这无穷个严格伪压缩映射的公共不动点,并且是变分不等式〈(I-A)x,J_q(p-x)〉≤0,p∈(n i=l)F(T_i)的解.论文推广和改进了一些前人的相应结论.

The authors consider a general composite iterative method for obtaining an infinite family of strictly pseudo-contractive mappings in q-uniformly smooth and strictly convex Banach spaces. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of fixed points, which solves the variational inequality 〈（I-A）x,J_q（p-x）〉≤0,p∈（n i=l）F（T_i）. The results improve and extend the i=1 corresponding ones announced by some others.