A New Iterative Method for Equilibrium Problems and Fixed Point Problems

Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong converg...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.251-259-126
Main Authors: Latif, Abdul, Eslamian, Mohammad
Format: Article
Language:English
Subjects:
Convergence (Mathematics)
Equilibrium
Fixed point theory
Hilbert space
Iterative methods (Mathematics)
Mappings (Mathematics)
Mathematical research
Mathematics
Optimization
Partial differential equations
Studies
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Summary:Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of Anh (2012), Cianciaruso et al. (2010), and many others.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/178053