Iterative methods for solving the generalized split common null point problem in Hilbert spaces

Reich, Simeon; Tuyen, Truong Minh

doi:10.1080/02331934.2019.1655562

Cited by 51 publications

(15 citation statements)

References 26 publications

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“…Furthermore, we obtain a strong convergence result of the problem and apply our result to equilibrium problems and zero point problems. The result obtained in this paper mainly extends and generalizes the results presented in [4,11,12,13].…”

Section: Introductionsupporting

confidence: 88%

“…In 2020, Reich and Tuyen [12] introduced the following generalized split common null point problem (for short, GSCNPP): For i = 1, 2, • • • , N, let H i be a real Hilbert space, and let B i : H i → 2 H i be a maximal monotone operator. Let T i : H i → H i+1 be a bounded linear operator for…”

Section: Introductionmentioning

confidence: 99%

“…For recent extensions, we refer to [22,23]. Motivated by the results presented in [11,12,13] and the ongoing research in this direction, we propose a self-adaptive inertial Halpern iterative method for finding the solution of split minimization problem with multiple output sets, which is also a common fixed point of a finite family of Bregman relatively nonexpansive mappings in the framework of p-uniformly convex and uniformly smooth Banach spaces. Furthermore, we obtain a strong convergence result of the problem and apply our result to equilibrium problems and zero point problems.…”

Section: Introductionmentioning

confidence: 99%

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Approximation of solutions of the split minimization problem with multiple output sets and common fixed point problems in real Banach spaces

2022

J. Nonlinear Var. Anal.

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In this paper, we introduce and study a split minimization problem with multiple output sets. We propose a new iterative method, which employs the inertial Halpern approximation technique, for a common solution of the split minimization problem and the fixed point problem with a finite family of Bregman relatively nonexpansive mappings in the framework of p-uniformly convex and uniformly smooth Banach spaces. Our iterative method uses the step sizes which do not require prior knowledge of the operators norm, and we prove a strong convergence result under some mild conditions. Moreover, we present some applications of our result and further demonstrate the efficiency and applicability of our algorithm with some numerical examples. The results presented in this paper unify and complement several existing results in the literature.

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Section: Introductionsupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximation of solutions of the split minimization problem with multiple output sets and common fixed point problems in real Banach spaces

2022

J. Nonlinear Var. Anal.

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“…In 2020, Reich and Tuyen [38] first introduced and studied the following generalized split feasibility problem (GSFP).…”

mentioning

confidence: 99%

“…In [38], Reich and Tuyen proved a strong convergence theorem for a modification of the CQ method which solves the GSFP (80). For more details on the GSFP (80), one can read the paper [38].…”

mentioning

confidence: 99%

Self adaptive inertial relaxed $ CQ $ algorithms for solving split feasibility problem with multiple output sets

Taddele

Rehman

Gebrie

2023

JIMO

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<p style='text-indent:20px;'>In this paper, we propose two new self-adaptive inertial relaxed <inline-formula><tex-math id="M2">\begin{document}$ CQ $\end{document}</tex-math></inline-formula> algorithms for solving the split feasibility problem with multiple output sets in the framework of real Hilbert spaces. The proposed algorithms involve computing projections onto half-spaces instead of onto the closed convex sets, and the advantage of the self-adaptive step size introduced in our algorithms is that it does not require the computation of operator norm. We establish and prove weak and strong convergence theorems for the iterative sequences generated by the introduced algorithms for solving the aforementioned problem. Moreover, we apply the new results to solve some other problems. Finally, we present some numerical examples to illustrate the implementation of our algorithms and compared them to some existing results.</p>

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A unified scheme for solving split inclusions with applications

Sumalai

Abubakar

Salisu

2023

Math Methods in App Sciences

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In this article, we propose an iterative scheme for solving a generalized split common null point problem. The iterative method uses self‐adaptive stepsizes that do not depend on the Lipschitz constants of the underlying operators. Instead, the stepsizes are updated using a simple updating formula. We prove the strong convergence theorems of the sequence generated by the iterative scheme under some mild assumptions. Furthermore, we derive iterative methods for solving split generalized variational inequality, convex feasibility, and minimization problems. In addition, some numerical illustrations are provided to support the main result.

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Iterative methods for solving the generalized split common null point problem in Hilbert spaces

Cited by 51 publications

References 26 publications

Approximation of solutions of the split minimization problem with multiple output sets and common fixed point problems in real Banach spaces

Approximation of solutions of the split minimization problem with multiple output sets and common fixed point problems in real Banach spaces

Self adaptive inertial relaxed $ CQ $ algorithms for solving split feasibility problem with multiple output sets

A unified scheme for solving split inclusions with applications

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