Our study in this paper is focused on the split equality fixed-point problem with firmly quasi-non-expansive operators in infinite-dimensional Hilbert spaces. A self-adaptive simultaneous scheme is introduced, and its...
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Our study in this paper is focused on the split equality fixed-point problem with firmly quasi-non-expansive operators in infinite-dimensional Hilbert spaces. A self-adaptive simultaneous scheme is introduced, and its weak convergence is established under mild and standard assumptions. The new proposed scheme generalizes and extends some related works in the literature, and its simple structure makes it easy for implementation and numerical testing. Primary experiments presented in this paper, in finite- and infinite-dimensional spaces, emphasize their practical advantages over existing results.
In this article, we first propose an extended split equality problem which is an extension of the convex feasibility problem, and then introduce a parameter w to establish the fixed point equation system. We show the ...
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In this article, we first propose an extended split equality problem which is an extension of the convex feasibility problem, and then introduce a parameter w to establish the fixed point equation system. We show the equivalence of the extended split equality problem and the fixed point equation system. Based on the fixed point equation system, we present a simultaneous iterative algorithm and obtain the weak convergence of the proposed algorithm. Further, by introducing the concept of a G-mapping of a finite family of strictly pseudononspreading mappings {T-i}(i=1)(N), we consider an extended split equality fixed point problem for G-mappings and give a simultaneous iterative algorithm with a way of selecting the stepsizes which do not need any prior information about the operator norms, and the weak convergence of the proposed algorithm is obtained. We apply our iterativealgorithms to some convex and nonlinear problems. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithms.
Let H-1, H-2, H-3 be real Hilbert spaces, let A:H-1 -> H-3, B:H-2 -> H-3 be two bounded linear operators. Moudafi introduced simultaneous iterative algorithms (Trans. Math. Program. Appl. 1:1-11, 2013) with weak...
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Let H-1, H-2, H-3 be real Hilbert spaces, let A:H-1 -> H-3, B:H-2 -> H-3 be two bounded linear operators. Moudafi introduced simultaneous iterative algorithms (Trans. Math. Program. Appl. 1:1-11, 2013) with weak convergence for the following split common fixed-point problem: find x is an element of F(U), y is an element of F(T) suchthat Ax = By, (1) where U:H-1 -> H-1 and T:H-2 -> H-2 are two firmly quasi-nonexpansive operators with nonempty fixed-point sets F(U) = {x is an element of H-1 : Ux = x} and F(T) = {x is an element of H-2 : Tx = x}. Note that by taking H-2 = H-3 and B = I, we recover the split common fixed-point problem originally introduced in Censor and Segal (J. Convex Anal. 16: 587-600, 2009). In this paper, we will continue to consider the split common fixed-point problem (1) governed by the general class of generalized asymptotically quasi-nonexpansive mappings. To estimate the norm of an operator is a very difficult, if it is not an impossible task. The purpose of this paper is to propose a simultaneous iterative algorithm with a way of selecting the stepsizes such that the implementation of the algorithm does not need any prior information as regards the operator norms.
Let H-1, H-2 and H-3 be real Hilbert spaces, let A : H-1. H-3 and B : H-2. H3 be two bounded linear operators. Moudafi introduced simultaneous iterative algorithms with weak convergence for the following split common ...
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Let H-1, H-2 and H-3 be real Hilbert spaces, let A : H-1. H-3 and B : H-2. H3 be two bounded linear operators. Moudafi introduced simultaneous iterative algorithms with weak convergence for the following split common fixed-point problem: Find x. F(U), y. F(T) such that Ax = By, (1) where U : H-1. H-1 and T : H2. H-2 are two firmly quasi-nonexpansive operators with nonempty fixed-point sets F(U) = {x. H1 : Ux = x} and F(T) = {x. H-2 : T x = x}. Note that, by taking H-2 = H-3 and B = I, we recover the split common fixed-point problem originally introduced by Cesnor and Segal. However, to employ Moudafi's algorithms, one needs to know a prior norm (or at least an estimate of the norm) of the bounded linear operators. To estimate the norm of an operator is very difficult, if it is not an impossible task. In this paper, we will continue to consider the split common fixed-point problem (1) governed by the general class of quasi-nonexpansive operators. We introduce a simultaneous iterative algorithm with a way of selecting the stepsizes such that the implementation of the algorithm does not need any prior information about the operator norms. The weak convergence result of algorithm is obtained and some applied nonlinear analysis examples are stated.
In this paper, we prove strong convergence theorem for approximation of solutions of split equality fixed point problems for infinite families of multi-valued quasi-nonexpansive mappings in real Hilbert spaces using a...
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In this paper, we prove strong convergence theorem for approximation of solutions of split equality fixed point problems for infinite families of multi-valued quasi-nonexpansive mappings in real Hilbert spaces using a new iterative scheme. Our iterative scheme is constructed with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norms. Our result extends and generalize many important recent results in this direction in the literature.
This paper deals with a general type of linear matrix equation problem. It presents new iterativealgorithms to solve the matrix equations of the form A(i) X B-i = F-i. These algorithms are based on the incremental su...
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This paper deals with a general type of linear matrix equation problem. It presents new iterativealgorithms to solve the matrix equations of the form A(i) X B-i = F-i. These algorithms are based on the incremental subgradient and the parallel subgradient methods. The convergence region of these algorithms are larger than other existing iterativealgorithms. Finally, some experimental results are presented to show the efficiency of the proposed algorithms.
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