Proximal point algorithm for infinite pseudo-monotone bifunctions |
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Authors: | Hadi Khatibzadeh Vahid Mohebbi |
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Institution: | 1. Department of Mathematics, University of Zanjan, Zanjan, Iran.hkhatibzadeh@znu.ac.ir;3. Department of Mathematics, University of Zanjan, Zanjan, Iran. |
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Abstract: | In this paper, first we study the weak convergence of the proximal point algorithm for an infinite family of equilibrium problems of pseudo-monotone type in Hilbert spaces. Then with additional conditions on the bifunctions, we prove the strong convergence for the family to a common equilibrium point. We also study a regularization of Halpern type and prove the strong convergence of the generated sequence to an equilibrium point of the family of infinite pseudo-monotone bifunctions without any additional assumptions on the bifunctions. A concrete example of a family of pseudo-monotone bifunctions is also presented. |
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Keywords: | Equilibrium problem pseudo-monotone bifunction proximal point algorithm weak convergence strong convergence Halpern’s method |
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