Implicit iterative method for approximating a common solution of split equilibrium problem and fixed point problem for a nonexpansive semigroup
نویسندگان
چکیده
منابع مشابه
A Method for a Solution of Equilibrium Problem and Fixed Point Problem of a Nonexpansive Semigroup in Hilbert's Spaces
Let C be a nonempty, closed, and convex subset of a real Hilbert space H . Denote the metric projection from x ∈ H onto C by PCx. Let T : C → C be a nonexpansive mapping on C, that is, T : C → C and ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. We use F T to denote the set of fixed points of T , that is, F T {x ∈ C : x Tx}. Let {T s : s > 0} be a nonexpansive semigroup on a closed convex subset C, tha...
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A New Iterative Method for the Split Common Fixed Point Problem in Hilbert Spaces
The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper, we propose a new algorithm that is completely different from the existing algorithms. Under standard assumptions, we establish a weak convergence theorem of the proposed algorith...
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We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real Hilbert spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common solution of the considered problems. A numerical example is presented to illustrate the convergence result. Our results improve...
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ژورنال
عنوان ژورنال: Arab Journal of Mathematical Sciences
سال: 2014
ISSN: 1319-5166
DOI: 10.1016/j.ajmsc.2013.04.002