Self-adaptive algorithms for the split problem of the quasi-pseudocontractive operators in Hilbert spaces

Sun, Wenlong; Lu, Gang; Jin, Yuanfeng; Park, Choonkil

doi:10.3934/math.2022487

MATH

2022

DOI: 10.3934/math.2022487

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Self-adaptive algorithms for the split problem of the quasi-pseudocontractive operators in Hilbert spaces

Wenlong Sun¹,

Gang Lu²,

Yuanfeng Jin³

et al.

Abstract: <abstract><p>Self-adaptive algorithms are presented for solving the split common fixed point problem of quasi-pseudocontractive operators in Hilbert spaces. Weak and strong convergence theorems are given under some mild assumptions.</p></abstract>

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Cited by 7 publications

References 27 publications

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A strongly convergent algorithm for solving split equality problems beyond monotonicity

Mewomo,

Uzor,

Gibali

2024

Comp. Appl. Math.

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In this paper, we focus on some split inverse problems, namely the split equality variational inequalities and common fixed point problems, and combine various operator theory techniques to establish minimum-norm strong convergence for our proposed method. We present two strong convergent results with (and without) reference to the monotonicity property of the cost operators. Our convergence analyses assume very mild conditions and thus generalize and extend recent related results in the literature. Furthermore, several numerical examples illustrate the practical potentials and advantages of our proposed algorithm.

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A strongly convergent algorithm for solving split equality problems beyond monotonicity

Mewomo,

Uzor,

Gibali

2024

Comp. Appl. Math.

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A self-adaptive relaxed primal-dual iterative algorithm for solving the split feasibility and the fixed point problem

Wang,

Huang,

Jiang

2024

Communications in Nonlinear Science and Numerical Simulation

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Two new self-adaptive algorithms for solving split common fixed point problems with multiple output sets

et al. 2023

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Self-adaptive algorithms for the split problem of the quasi-pseudocontractive operators in Hilbert spaces

Abstract: <abstract><p>Self-adaptive algorithms are presented for solving the split common fixed point problem of quasi-pseudocontractive operators in Hilbert spaces. Weak and strong convergence theorems are given under some mild assumptions.</p></abstract>

Cited by 7 publications

References 27 publications

A strongly convergent algorithm for solving split equality problems beyond monotonicity

A strongly convergent algorithm for solving split equality problems beyond monotonicity

A self-adaptive relaxed primal-dual iterative algorithm for solving the split feasibility and the fixed point problem

Two new self-adaptive algorithms for solving split common fixed point problems with multiple output sets

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