Three-step iterations for variational inequalities and nonexpansive mappings |
| |
Authors: | Muhammad Aslam Noor Yonghong Yao |
| |
Institution: | aMathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan bDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China |
| |
Abstract: | In this paper, we introduce a new three-step iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality using the technique of updating the solution. We show that the sequence converges strongly to a common element of two sets under some control conditions. Results proved in this paper may be viewed as an improvement and refinement of the recent results of Noor and Huang M. Aslam Noor, Z. Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput., in press] and Yao and Yao Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput., in press]. |
| |
Keywords: | Nonexpansive mapping Monotone mapping Variational inequality Strong convergence |
本文献已被 ScienceDirect 等数据库收录! |
|