The split common fixed point problem for multivalued demicontractive mappings and its applications

In this work, we study the split common fixed point problem which was first introduced by Censor and Segal [14]. We introduce an algorithm based on the viscosity approximation method without prior knowledge of the operator norm by selecting the stepsizes in the same adaptive way as L?opez et al. [22] for solving the problem for two attracting quasi-nonexpansive operators in real Hilbert spaces. A strong convergence result of the proposed algorithm is established under some suitable conditions. We also modify our algorithm to extend to the class of demicontractive operators and the class of hemicontractive operators, and obtain strong convergence results. Moreover, we apply our main result to other split problems, that is, the split feasibility problem and the split variational inequality problem. Finally, a numerical result is also given to illustrate the convergence behavior of our algorithm.

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“…Since x n j u, it follows from ( 21) that y n j u. From (20) and by the demiclosedness of I − S at 0, we get u ∈ F(S). Therefore, u ∈ Γ.…”

Section: Theorem 32mentioning

confidence: 94%

Viscosity approximation methods for split common fixed point problems without prior knowledge of the operator norm

Jailoka

Suantai

2020

Filomat

Self Cite

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“…If S(a) only contains a, then we refer to a as a strict fixed point of S. The study of strictly fixed points for a specific type of contractive mappings was first conducted by Aubin and Siegel [27]. Since then, this condition has been rapidly applied to various multivalued mappings, such as those in [28][29][30].…”

Section: Preliminariesmentioning

confidence: 99%

An Algorithm That Adjusts the Stepsize to Be Self-Adaptive with an Inertial Term Aimed for Solving Split Variational Inclusion and Common Fixed Point Problems

Ngwepe,

Jolaoso,

Aphane

et al. 2023

Mathematics

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In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every iteration, and the stepsize is defined self-adaptively without a prior estimate of the Lipschitz constant. A convergence theorem is demonstrated to be strong even under lenient conditions and to showcase the suggested method’s efficiency and precision. Some numerical tests are given. Moreover, the significance of the proposed method is demonstrated through its application to an image reconstruction issue.

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“…All computations are carried out using Matlab version 2017(a) on a HP personal computer. We start by giving the following example of multivalued λ-demicontractive mapping given by Jailoka and Suntai in [48]. Let H = R, and…”

Section: Numerical Examplementioning

confidence: 99%

A self adaptive inertial subgradient extragradient algorithm for variational inequality and common fixed point of multivalued mappings in Hilbert spaces

Jolaoso

Taiwo

Alakoya

2019

Demonstratio Mathematica

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We consider a new subgradient extragradient iterative algorithm with inertial extrapolation for approximating a common solution of variational inequality problems and fixed point problems of a multivalued demicontractive mapping in a real Hilbert space. We established a strong convergence theorem for our proposed algorithm under some suitable conditions and without prior knowledge of the Lipschitz constant of the underlying operator. We present numerical examples to show that our proposed algorithm performs better than some recent existing algorithms in the literature.

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The split common fixed point problem for multivalued demicontractive mappings and its applications

Cited by 13 publications

References 29 publications

Viscosity approximation methods for split common fixed point problems without prior knowledge of the operator norm

Viscosity approximation methods for split common fixed point problems without prior knowledge of the operator norm

An Algorithm That Adjusts the Stepsize to Be Self-Adaptive with an Inertial Term Aimed for Solving Split Variational Inclusion and Common Fixed Point Problems

A self adaptive inertial subgradient extragradient algorithm for variational inequality and common fixed point of multivalued mappings in Hilbert spaces

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