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Hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense |
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| Authors: | Lu-Chuan Ceng Sy-Ming Guu Jen-Chih Yao |
| Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China 2. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, 200234, China 3. Graduate Institute of Business and Management, College of Management, Chang Gung University, Kwei Shan, Taoyuan Hsien, Taiwan 4. Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung, 807, Taiwan 5. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jidda, Saudi Arabia |
| Abstract: | In this paper we introduce an iterative algorithm for finding a common element of the fixed point set of an asymptotically strict pseudocontractive mapping S in the intermediate sense and the solution set of the minimization problem (MP) for a convex and continuously Frechet differentiable functional in Hilbert space. The iterative algorithm is based on several well-known methods including the extragradient method, CQ method, Mann-type iterative method and hybrid gradient projection algorithm with regularization. We obtain a strong convergence theorem for three sequences generated by our iterative algorithm. In addition, we also prove a new weak convergence theorem by a modified extragradient method with regularization for the MP and the mapping S. |
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