A general composite iterative method for strictly pseudocontractive mappings in Hilbert spaces

作者：Jung Jong Soo^*

来源：Fixed Point Theory and Applications, 2014, 2014(1): 173.

DOI：10.1186/1687-1812-2014-173

• composite iterative method
• k-strictly pseudocontractive mapping
• nonexpansive mapping
• fixed points
• Lipschitzian
• weakly asymptotically regular
• rho-Lipschitzian and eta-strongly monotone operator
• strongly positive bounded linear operator
• Hilbert space
• variational inequality

In this paper, we introduce a new general composite iterative method for finding a fixed point of a strictly pseudocontractive mapping in Hilbert spaces. We establish the strong convergence of the sequence generated by the proposed iterative method to a fixed point of the mapping, which is the unique solution of a certain variational inequality. In particular, we utilize weaker control conditions than previous ones in order to show strong convergence. Our results complement, develop, and improve upon the corresponding ones given by some authors recently in this area.

• 出版日期2014-8-18