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22-04-2019 | Original Paper | Issue 2/2020

A new algorithm for solving the split common null point problem in Hilbert spaces

Journal:: Numerical Algorithms > Issue 2/2020

Authors:: Simeon Reich, Truong Minh Tuyen

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Abstract

We study the split common null point problem in two Hilbert spaces. In order to solve this problem, we propose a new algorithm and establish a strong convergence theorem for it. Our scheme combines the hybrid projection method with the proximal point algorithm.

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Agarwal, R.P., O’Regan, D., Sahu, D.R.: Fixed Point Theory for Lipschitzian-type Mappings with Applications. Springer, New York (2009) MATH

Barbu, V., Precupanu, T. h.: Convexity and Optimization in Banach Spaces. Editura Academiei R. S. R., Bucharest (1978) MATH

Boikanyo, O.A.: A strongly convergent algorithm for the split common fixed point problem. Appl. Math. Comput. 265, 844–853 (2015) MathSciNetMATH

Byrne, C.: Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Problems 18, 441–453 (2002) MathSciNetCrossRef

Byrne, C.: A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Problems 18, 103–120 (2004) MathSciNetCrossRef

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

Censor, Y., Elfving, T.: A multi projection algorithm using Bregman projections in a product space. Numer. Algorithms 8, 221–239 (1994) MathSciNetCrossRef

Censor, Y., Elfving, T., Kopf, N., Bortfeld, T.: The multiple-sets split feasibility problem and its application. Inverse Problems 21, 2071–2084 (2005) MathSciNetCrossRef

Censor, Y., Gibali, A., Reich, S.: Algorithms for the split variational inequality problems. Numer. Algorithms 59, 301–323 (2012) MathSciNetCrossRef

10.

Censor, Y., Segal, A.: The split common fixed point problem for directed operators. J. Convex Anal. 16, 587–600 (2009) MathSciNetMATH

11.

Cui, H., Su, M.: On sufficient conditions ensuring the norm convergence of an iterative sequence to zeros of accretive operators. Appl. Math. Comp. 258, 67–71 (2015) MathSciNetCrossRef

12.

Cui, H., Wang, F.: Iterative methods for the split common fixed point problem in Hilbert spaces. Fixed Point Theory Appl. 2014, 1–8 (2014) MathSciNetCrossRef

13.

Dadashi, V.: Shrinking projection algorithms for the split common null point problem. Bull. Aust. Math. Soc. 99, 299–306 (2017) MathSciNetCrossRef

14.

Goebel, K., Kirk, W.A.: Topics in Metric Fixed Point Theory, Cambridge Stud. Adv Math., vol. 28. Cambridge Univ. Press, Cambridge (1990) CrossRef

15.

Goebel, K., Reich, S.: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings. Marcel Dekker, New York (1984) MATH

16.

López, G., Martín-Márquez, V., Wang, F., Xu, H. -K.: Solving the split feasibility problem without prior knowledge of matrix norms. Inverse Probems 28, 085004 (2012) MathSciNetCrossRef

17.

Masad, E., Reich, S.: A note on the multiple-set split convex feasibility problem in Hilbert space. J. Nonlinear Convex Anal. 8, 367–371 (2007) MathSciNetMATH

18.

Moudafi, A.: The split common fixed point problem for demicontractive mappings. Inverse Problems 055007, 26 (2010) MathSciNetMATH

19.

Rockafellar, R.T.: On the maximal monotonicity of subdifferential mappings. Pacific J. Math. 33, 209–216 (1970) MathSciNetCrossRef

20.

Rockafellar, R.T.: On the maximality of sums of nonlinear monotone operators. Trans. Amer. Math. Soc. 149, 75–88 (1970) MathSciNetCrossRef

21.

Schopfer, F., Schuster, T., Louis, A.K.: An iterative regularization method for the solution of the split feasibility problem in Banach spaces. Inverse Problems 055008, 24 (2008) MathSciNetMATH

22.

Shehu, Y., Iyiola, O.S., Enyi, C.D.: An iterative algorithm for solving split feasibility problems and fixed point problems in Banach spaces. Numer. Algorithms 72, 835–864 (2016) MathSciNetCrossRef

23.

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

24.

Takahashi, W.: The split feasibility problem in Banach spaces. J. Nonlinear Convex Anal. 15, 1349–1355 (2014) MathSciNetMATH

25.

Takahashi, W.: The split feasibility problem and the shrinking projection method in Banach spaces. J. Nonlinear Convex Anal. 16, 1449–1459 (2015) MathSciNetMATH

26.

Takahashi, S., Takahashi, W.: The split common null point problem and the shrinking projection method in Banach spaces. Optimization 65, 281–287 (2016) MathSciNetCrossRef

27.

Takahashi, W.: The split common null point problem in Banach spaces. Arch. Math. 104, 357–365 (2015) MathSciNetCrossRef

28.

Wang, F.: A new algorithm for solving the multiple-sets split feasibility problem in Banach spaces. Numer. Funct. Anal. Optim. 35, 99–110 (2014) MathSciNetCrossRef

29.

Wang, F.: A new iterative method for the split common fixed point problem in Hilbert spaces. Optimization 66, 407–415 (2017) MathSciNetCrossRef

30.

Wang, F., Xu, H.K.: Cyclic algorithms for split feasibility problems in Hilbert spaces. Nonlinear Anal. 74, 4105–4111 (2011) MathSciNetCrossRef

31.

Xu, H.K.: A variable Krasnosel’skii-Mann algorithm and the multiple-set split feasibility problem. Inverse Problems 22, 2021–2034 (2006) MathSciNetCrossRef

32.

Xu, H.K.: Iterative methods for the split feasibility problem in infinite dimensional Hilbert spaces. Inverse Problems 105018, 26 (2010) MathSciNet

33.

Yang, Q.: The relaxed CQ algorithm for solving the split feasibility problem. Inverse Problems 20, 1261–1266 (2004) MathSciNetCrossRef

34.

Yosida, K.: Functional Analysis. Springer, Berlin (1980) MATH

Title: A new algorithm for solving the split common null point problem in Hilbert spaces
Authors:: Simeon Reich
Truong Minh Tuyen
Publication date: 22-04-2019
DOI: https://doi.org/10.1007/s11075-019-00703-z
Publisher: Springer US
Journal: Numerical Algorithms
Issue 2/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265

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