On the weak and strong convergence of the proximal point algorithm in reflexive Banach spaces
Authors:
- 12 June 2017
- journal article
- research article
- Published by Taylor & Francis in Optimization
- Vol. 66 (9) , 1487-1494
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
Funding Information
- the Sari Branch, Islamic Azad Universit
This publication has 22 references indexed in Scilit:
- Finite termination of the proximal point algorithm in Banach spacesJournal of Mathematical Analysis and Applications, 2012
- On convergence of the proximal point algorithm in Banach spacesProceedings of the American Mathematical Society, 2011
- Maximal monotonicity of bifunctionsOptimization, 2010
- Another version of the proximal point algorithm in a Banach spaceNonlinear Analysis, 2009
- On Finite and Strong Convergence of a Proximal Method for Equilibrium ProblemsNumerical Functional Analysis and Optimization, 2007
- Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spacesNonlinear Analysis, 2007
- Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spacesJournal of Mathematical Analysis and Applications, 2007
- Existence theorems for m-accretive operators in Banach spacesJournal of Mathematical Analysis and Applications, 2005
- Iterative Algorithms for Nonlinear OperatorsJournal of the London Mathematical Society, 2002
- Strong convergence of resolvents of monotone operators in Banach spacesProceedings of the American Mathematical Society, 1988