Strong convergence of approximated iterations for asymptotically pseudocontractive mappings

作者：Yao, Yonghong; Postolache, Mihai; Kang, Shin Min^*

来源：Fixed Point Theory and Applications, 2014, 2014(1): 100.

DOI：10.1186/1687-1812-2014-100

• asymptotically pseudocontractive mappings
• iterative algorithms
• fixed point
• Hilbert space

The asymptotically nonexpansive mappings have been introduced by Goebel and Kirk in 1972. Since then, a large number of authors have studied the weak and strong convergence problems of the iterative algorithms for such a class of mappings. It is well known that the asymptotically nonexpansive mappings is a proper subclass of the class of asymptotically pseudocontractive mappings. In the present paper, we devote our study to the iterative algorithms for finding the fixed points of asymptotically pseudocontractive mappings in Hilbert spaces. We suggest an iterative algorithm and prove that it converges strongly to the fixed points of asymptotically pseudocontractive mappings.

• 出版日期2014-5-2
• 单位天津工业大学