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On the weak and strong convergence of the proximal point algorithm in reflexive Banach spaces

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Abstract In this paper, some proximal point algorithms (PPAs) for maximal monotone operators in Banach spaces are considered. We obtain some results on the boundedness and the convergence of sequences… Click to show full abstract

Abstract In this paper, some proximal point algorithms (PPAs) for maximal monotone operators in Banach spaces are considered. We obtain some results on the boundedness and the convergence of sequences generated by the PPAs with some assumptions. We can also get zero of maximal -expansive operator and maximal -monotone at zero operator using this method and then we apply it for finding a solution of the equilibrium problem.

Keywords: strong convergence; proximal point; weak strong; banach spaces

Journal Title: Optimization
Year Published: 2017

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