New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators

作者：Su Yongfu^*; Li Mengqin; Zhang Hong

来源：Applied Mathematics and Computation, 2011, 217(12): 5458-5465.

DOI：10.1016/j.amc.2010.12.015

• Hemi-relatively nonexpansive mapping
• Generalized projection
• Monotone hybrid algorithm
• Cauchy sequence
• Maximal monotone operator

The purpose of this article is to prove the strong convergence theorems for hemi-relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems for hemi-relatively nonexpansive mappings, a new monotone hybrid iteration algorithm is presented and is used to approximate the fixed point of hemi-relatively nonexpansive mappings. Noting that, the general hybrid iteration algorithm can be used for relatively nonexpansive mappings but it can not be used for hemi-relatively nonexpansive mappings. However, this new monotone hybrid algorithm can be used for hemi-relatively nonexpansive mappings. In addition, a new method of proof has been used in this article. That is, by using this new monotone hybrid algorithm, we firstly claim that, the iterative sequence is a Cauchy sequence. The results of this paper modify and improve the results of Matsushita and Takahashi, and some others.

• 出版日期2011-2-15
• 单位天津工业大学