An iterative scheme for split variational inclusion and fixed point problem for demicontractive mappings

Lijuan ZHANG , Junmin CHEN

Front. Math. China ›› 2025, Vol. 20 ›› Issue (4) : 199 -211.

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Front. Math. China ›› 2025, Vol. 20 ›› Issue (4) :199 -211. DOI: 10.3868/s140-DDD-025-0016-x
RESEARCH ARTICLE
An iterative scheme for split variational inclusion and fixed point problem for demicontractive mappings
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Abstract

In this paper, an iterative algorithm is introduced to find a common solution for the split variational inclusion problem and the fixed-point problem of a countable family of demicontractive mappings in Hilbert spaces. As a result, strong convergence theorem concerning the common element along with its applications and numerical examples is obtained.

Keywords

Split variational inclusion / demicontractive mapping / fixed point

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Lijuan ZHANG, Junmin CHEN. An iterative scheme for split variational inclusion and fixed point problem for demicontractive mappings. Front. Math. China, 2025, 20(4): 199-211 DOI:10.3868/s140-DDD-025-0016-x

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References

[1]

Byrne C., Censor, Y., Gibali, A. , Reich, S. . The split common null point problem. J. Nonlinear Convex Anal. 2012; 13(4): 759–775

[2]

Combettes P.L. , Hirstoaga, S.A. . Equilibrium programming in Hilbert spaces. J. Nonlinear Convex Anal. 2005; 6(1): 117–136

[3]

Deepho J., Thounthong, P., Kumam, P. , Phiangsungnoen, S. . A new general iterative scheme for split variational inclusion and fixed point problems of k-strict pseudocontraction mappings with convergence analysis. J. Comput. Appl. Math. 2017; 318: 293–306

[4]

Kazmi K.R. , Rizvi, S.H. . An iterative method for split variational inclusion problem and fixed point problem for a nonexpansive mapping. Optim. Lett. 2014; 8(3): 1113–1124

[5]

Maingé . Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization. Set-Valued Anal. 2008; 16(7/8): 899–912

[6]

Marino G. , Xu, H.K. . A general iterative method for nonexpansive mappings in Hilbert spaces. J. Math. Anal. Appl. 2006; 318(1): 43–52

[7]

Marino G. , Xu, H.K. . Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl. 2007; 329(1): 336–346

[8]

Moudafi A. . Split monotone variational inclusions. J. Optim. Theory Appl. 2011; 150(2): 275–283

[9]

Takahashi S., Takahashi, W. , Toyoda, M. . Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces. J. Optim. Theory Appl. 2010; 147(1): 27–41

[10]

Xu H.K. . An iterative approach to quadratic optimization. J. Optim. Theory Appl. 2003; 116(3): 659–678

[11]

Zegeye H. , Shahzad, N. . Convergence of Mann’s type iteration method for generalized asymptotically nonexpansive mappings. Comput. Math. Appl. 2011; 62(11): 4007–4014

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