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Abstract
The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for a relaxed cocoercive mapping in a real Hilbert space. In addition, we obtain some applications by using this result. The results obtained in this paper generalize and refine some known results in the current literature.
Highlights
Let H be a real Hilbert space, whose inner product and norm are denoted by, and, respectively
The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for a relaxed cocoercive mapping in a real Hilbert space
A typical problem is that of minimizing a quadratic function over the set of the fixed points of a nonexpansive mapping on a real Hilbert space H : min x Fix S
Summary
Let H be a real Hilbert space, whose inner product and norm are denoted by , and , respectively. A typical problem is that of minimizing a quadratic function over the set of the fixed points of a nonexpansive mapping on a real Hilbert space H : min x Fix S They proved that the sequence xn generated by iterative scheme (1.4) converges strongly to the unique solution of the variational inequality. Motivated by the recent works, we introduce a more general iterative algorithm for finding a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of a mixed equilibrium problem, and the set of solutions of the variational inequality problem for a relaxed cocoercive mapping in a real Hilbert space. The scheme is defined as follows: x1 H and n 1, C,
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