Abstract
In this paper, we introduce a new iterative method in a real Hilbert space for approximating a point in the solution set of a pseudomonotone equilibrium problem which is a common fixed point of a finite family of demicontractive mappings. Our result does not require that we impose the condition that the sum of the control sequences used in the finite convex combination is equal to 1. Furthermore, we state and prove a strong convergence result and give some numerical experiments to demonstrate the efficiency and applicability of our iterative method.
Highlights
In this paper, we will always take C to be a nonempty closed and convex subset of a real Hilbert space H endowed with inner product 〈·, ·〉 and induced norm ‖·‖, and F(T) denotes the set of fixed points of a mapping T: C ⟶ C, that is, F(T) ≔ {x ∈ C: x Tx}.Definition 1
Let K be a nonempty closed and convex subset of a real Hilbert space H
In this paper, motivated by the works of Anh and Muu [25] and Wangkeeree et al [26], we propose an iterative algorithm for finding a common element in the set of fixed points of a finite family of demicontractive mappings, which solves equilibrium problems for pseudomonotone bifunctions and prove a strong convergence result which does not require such condition as in (15) on the control sequences
Summary
We will always take C to be a nonempty closed and convex subset of a real Hilbert space H endowed with inner product 〈·, ·〉 and induced norm ‖·‖, and F(T) denotes the set of fixed points of a mapping T: C ⟶ C, that is, F(T) ≔ {x ∈ C: x Tx}. Is it possible to give an iterative algorithm and obtain a strong convergence result for finding a common element in the set of fixed points of a finite family of demicontractive mappings which solves equilibrium problems for pseudomonotone bifunctions without imposing the type of condition in (15) on the control sequences?. In this paper, motivated by the works of Anh and Muu [25] and Wangkeeree et al [26], we propose an iterative algorithm for finding a common element in the set of fixed points of a finite family of demicontractive mappings, which solves equilibrium problems for pseudomonotone bifunctions and prove a strong convergence result which does not require such condition as in (15) on the control sequences. We further give a numerical experiment to demonstrate the performance of our iterative algorithm
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