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On difference of two monotone operators |
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| Authors: | Muhammad Aslam Noor Khalida Inayat Noor Abdelouahed Hamdi Eman H. El-Shemas |
| Affiliation: | (1) Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan;(2) Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, Safat, Kuwait;(3) Department of Mathematics, College of Basic Sciences, Main Campus, Shamiya, Kuwait |
| Abstract: | In this paper, we introduce and consider the problem of finding zeroes of difference of two monotone operators in a Hilbert space. Using the resolvent operator technique, we show that this problem is equivalent to the fixed point problem. This equivalence is used to suggest and analyze an iterative method for finding a zero of difference of two monotone operators. We also discuss the convergence of the iterative method under suitable conditions. Our method of proof is very simple as compared with other techniques. |
| Keywords: | Monotone operators Iterative method Resolvent operator Convergence |
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