Abstract
In this paper, we suggest and analyze an iterative scheme for finding an approximate element of the common set of solutions of a split equilibrium problem, a variational inequality problem and a hierarchical fixed point problem in a real Hilbert space. We also consider the strong convergence of the proposed method under some conditions. Results proved in this paper may be viewed as an improvement and refinement of the previously known results. MSC:49J30, 47H09, 47J20.
Highlights
Let H be a real Hilbert space, whose inner product and norm are denoted by ·, · and·
We have a variety of techniques to suggest and analyze various iterative algorithms for solving variational inequalities and the related optimization problems; see [ – ]
Kazmi and Rivzi [ ], Yao et al [ ] and Gu et al [ ] and by the recent work going on in this direction, we give an iterative method for finding an approximate element of the common set of solutions of ( ), ( )-( ) and ( ) for a strictly pseudo-contraction mapping in a real Hilbert space
Summary
Let H be a real Hilbert space, whose inner product and norm are denoted by ·, · and. ·. By changing the restrictions on parameters, the authors obtained another result on the iterative scheme ( ), the sequence {xn} generated by ( ) converges strongly to a point z ∈ F(T), which is the unique solution of the following variational inequality:. Kazmi and Rivzi [ ], Yao et al [ ] and Gu et al [ ] and by the recent work going on in this direction, we give an iterative method for finding an approximate element of the common set of solutions of ( ), ( )-( ) and ( ) for a strictly pseudo-contraction mapping in a real Hilbert space. [ ] Let H be a Hilbert space, C be a closed and convex subset of H, and T : C → C be a k-strict pseudo-contraction mapping.
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