A general iterative algorithm for an infinite family of nonexpansive operators in Hilbert spaces

作者：Zhang Cuijie^*; He Songnian

来源：Fixed Point Theory and Applications, 2013, 2013(1): 138.

DOI：10.1186/1687-1812-2013-138

• an infinite family of nonexpansive operators
• strong convergence
• k-Lipschitizian
• eta-strongly monotone
• split common fixed point problem

In this paper, we introduce a new general iterative algorithm for an infinite family of nonexpansive operators in Hilbert spaces. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to a common point of the sets of fixed points, which solves a variational inequality. Our results improve and extend the corresponding results announced by many others. As applications, at the end of the paper, we apply our results to the split common fixed point problem.

• 出版日期2013
• 单位中国民航大学