In this paper, we give a simple proof of Wang's recent result concerning split common fixed-point problems (F. Wang, J fixedpoint Theory Appl 19(4): 2427-2436, 2017). Moreover, we provide a more general sufficien...
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In this paper, we give a simple proof of Wang's recent result concerning split common fixed-point problems (F. Wang, J fixedpoint Theory Appl 19(4): 2427-2436, 2017). Moreover, we provide a more general sufficient condition than Wang's for the weak convergence to a solution of a split common fixed-point problem.
In this paper, we study the split common fixed-point problem of quasi-nonexpansive operators in Hilbert space. We establish a weak convergence theorem of the proposed iterative algorithm, which combines the primal-dua...
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In this paper, we study the split common fixed-point problem of quasi-nonexpansive operators in Hilbert space. We establish a weak convergence theorem of the proposed iterative algorithm, which combines the primal-dual method and the inertial method. In our algorithm, the step sizes are chosen self-adaptively so that the implementation of the algorithm does not need any prior information about bounded linear operator norms. Finally, numerical results are included to illustrate the efficiency of the proposed algorithm.
In this paper, A new cyclic iterative algorithm for split common fixed-point problems of demicontractive mappings is investigated. A strong convergence theorem with no compactness assumptions on the spaces or the mapp...
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In this paper, A new cyclic iterative algorithm for split common fixed-point problems of demicontractive mappings is investigated. A strong convergence theorem with no compactness assumptions on the spaces or the mappings and with no extra conditions on fixed-point sets is established in real Hilbert spaces.
In this work, we establish two new self-adaptive parallel algorithms to solve the generalized splitcommonfixedpointproblem which is to find a point which belongs to the intersection of finite family of fixedpoint...
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In this work, we establish two new self-adaptive parallel algorithms to solve the generalized splitcommonfixedpointproblem which is to find a point which belongs to the intersection of finite family of fixedpoint sets of demimetric mappings such that its image under a finite number of linear transformations belongs to the intersection of another finite family of fixedpoint sets of demimetric mappings in the image space. Under suitable assumptions, the weak and strong convergence theorems are analysed. The obtained results generalize and improve the recent results announced by many other authors in the framework of split inverse problem. As a direct consequence of our two main algorithms, we obtain several new algorithms. Preliminary numerical experiments are provided to illustrate the efficiency and implementation of our new methods and also to compare with others.
In this paper, we use the dual variable to propose a self-adaptive iterative algorithm for solving the splitcommonfixedpointproblems of averaged mappings in real Hilbert spaces. Under suitable conditions, we get t...
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In this paper, we use the dual variable to propose a self-adaptive iterative algorithm for solving the splitcommonfixedpointproblems of averaged mappings in real Hilbert spaces. Under suitable conditions, we get the weak convergence of the proposed algorithm and give applications in the split feasibility problem and the split equality problem. Some numerical experiments are given to illustrate the efficiency of the proposed iterative algorithm. Our results improve and extend the corresponding results announced by many others.
In this paper, we use the dual variable to propose two algorithms for split common fixed-point problems of averaged mappings in real Hilbert spaces. Under suitable conditions, weak and strong convergence theorems are ...
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In this paper, we use the dual variable to propose two algorithms for split common fixed-point problems of averaged mappings in real Hilbert spaces. Under suitable conditions, weak and strong convergence theorems are established. Finally, we give numerical experiments to illustrate the efficiency of the proposed iterative algorithms.
Very recently, Moudafi (Nonlinear Analysis 79 (2013) 117-121) introduced a relaxed alternating CQ-algorithm (RACQA) with weak convergence for the following convex feasibility problem: (1.1) Find x epsilon C, y epsilon...
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Very recently, Moudafi (Nonlinear Analysis 79 (2013) 117-121) introduced a relaxed alternating CQ-algorithm (RACQA) with weak convergence for the following convex feasibility problem: (1.1) Find x epsilon C, y epsilon Q such that Ax = By, where H-1, H-2 H-3 are real Hilbert spaces, C subset of H-1, Q subset of H-2 are two nonempty, closed and convex level sets, and A : H-1 -> H-3, B : H-2 -> H-3 are two bounded linear operators. In this paper, we will continue to consider the problem (1.1) and obtain a strongly convergent iterative sequence of Halpena-type to a solution of the problem and provide an affirmative answer to an open question posed by Moudafi in his recent work for convex feasibility problems in real Hilbert spaces. Furthermore, we study Halpern-type iterative schemes for finding common solutions of a convex feasibility problem and commonfixedpoints of an infinite family of quasi-nonexpansive mappings in Hilbert spaces. Our results improve and generalize many known results in the current literature.
In the present paper, we explore operator norm independent inertial type accelerated iterative algorithm solving generalized splitcommonfixedpointproblem, which is the problem of finding a point that belongs to th...
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In the present paper, we explore operator norm independent inertial type accelerated iterative algorithm solving generalized splitcommonfixedpointproblem, which is the problem of finding a point that belongs to the intersection of a finite family of fixedpoint sets of demimetric mappings such that its image under a finite number of linear transformations belongs to the intersection of another finite family of fixedpoint sets of demimetric mappings in the image space. We adopt rules for selecting the step size such that the implementation of our proposed algorithm does not need any prior information about the operator norms. The strong convergence result is analyzed and some applications of our proposed algorithm are demonstrated. Our result in this paper will improve and generalize many results in the literature. Numerical experiments show that our iteration method is very effective for approximating the solution point of problem under consideration.
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