We introduce two modifications of the Mann iteration, by using the hybrid methods, for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings in a Hilbert space. Then, we prove that such two sequences converge strongly to a common element of the set of solutions of an equilibrium problem and the set of common fixed points of an infinite family of asymptotically nonexpansive mappings. Our results improve and extend the results announced by many others.
In this article, we introduce a new iterative scheme with Meir-Keeler contractions for strict pseudo-contractions in Hilbert spaces. We also discuss the strong convergence theorems of the new iterative scheme for variational inequality problems in Hilbert spaces. The methods in this article are interesting and are different from those given in many other articles. Our results improve and extend the corresponding results announced by many others. MR(2000) Subject Classification: 47H09; 47H10.
We introduce a new monotone mapping in Banach spaces, which is an extension of the -monotone mapping studied by Nazemi (2012), and we generalize the variational inclusion involving the -monotone mapping. Based on the new monotone mapping, we propose a new proximal mapping which combines the proximal mapping studied by Nazemi (2012) with the mapping studied by Lan et al. ( 2011) and show its Lipschitz continuity. Based on the new proximal mapping, we give an iterative algorithm. Furthermore, we prove the convergence of iterative sequences generated by the algorithm under some appropriate conditions. Our results improve and extend corresponding ones announced by many others.
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