WEAK CONVERGENCE THEOREMS FOR GENERALIZED HYBRID MAPPINGS IN BANACH SPACES

Authors

  • W. Takahashi Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Japan and Applied Mathematics, National Sun Yaysen University, Taiwan
  • J.-C. Yao Department of Applied Mathematics, National Sun Yatsen University, Kaohsiung 80424, Taiwan

Abstract

Let E be a real Banach space and let C be a nonempty subset of E. A mapping T is called generalized hybrid if there are \alpha, \beta \in R such that \alpha\|Tx-Ty\|^2 + (1-\alpha)\|x-Tx\|^2 \leq \beta\|Tx-y\|^2 + (1-\beta)\|x-y\|^2 for all x,y \in C. In this paper, we first deal with some properties for generalized hybrid mappings in a Banach space. Then, we prove weak convergence theorems of Mann's type for such mappings in a Banach space satisfying Opial's condition.

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Published

2011-12-21

How to Cite

Takahashi, W., & Yao, J.-C. (2011). WEAK CONVERGENCE THEOREMS FOR GENERALIZED HYBRID MAPPINGS IN BANACH SPACES. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 2(1), 155-166. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/40

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Section

Research Article