Degree of convergence of modified averaged iterations for fixed points problems and operator equations |
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Authors: | Songnian He Jing Zhao Zhiming Li |
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Institution: | Civil Aviation University of China, College of Science, Jinbei Road 2898, 300300 Tianjin, PR China |
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Abstract: | Let H be a real Hilbert space. We propose a modification for averaged mappings to approximate the unique fixed point of a mapping T:H→H such that T is boundedly Lipschitzian and −T is monotone. We not only prove strong convergence theorems, but also determine the degree of convergence. Using this result, an iteration process is given for finding the unique solution of the equation Ax=f, where A:H→H is strongly monotone and boundedly Lipschitzian. |
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Keywords: | 47H09 47H10 |
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