Abstract
In this paper, we introduce new implicit and explicit iterative schemes for finding a common element of the set of solutions of the mixed equilibrium problem and the set of fixed points of a k-strictly pseudocontractive non-self mapping in Hilbert spaces. We establish results of the strong convergence of the sequences generated by the proposed schemes to a common point of two sets, which is a solution of a certain variational inequality. Our results extend and improve the corresponding results given by many authors recently in this area.
Highlights
Let H be a real Hilbert space with inner product ·, · and induced norm ·
By using the ideas of Marino and Xu [ ], Tien [, ] and Ceng et al [ ] provided the general iterative schemes for finding a fixed point of the nonexpansive mapping, which is a solution of a certain variational inequality related to a Lipschitzian and strongly monotone operator
Cho et al [ ] and Jung [, ] gave the general iterative schemes for finding a fixed point of the k-strictly pseudocontractive mapping, which is a solution of a certain variational inequality
Summary
Let H be a real Hilbert space with inner product ·, · and induced norm ·. By using the ideas of Marino and Xu [ ], Tien [ , ] and Ceng et al [ ] provided the general iterative schemes for finding a fixed point of the nonexpansive mapping, which is a solution of a certain variational inequality related to a Lipschitzian and strongly monotone operator.
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