Convergence theorems for finding the split common null point in Banach spaces

Suthep Suantai; Kittipong Srisap; Natthapong Naprang; Manatsawin Mamat; Vithoon Yundon; Prasit Cholamjiak

doi:10.4995/agt.2017.7257

Authors

Suthep Suantai Chiang Mai University
Kittipong Srisap University of Phayao
Natthapong Naprang University of Phayao
Manatsawin Mamat University of Phayao
Vithoon Yundon University of Phayao
Prasit Cholamjiak School of Science, University of Phayao

DOI:

https://doi.org/10.4995/agt.2017.7257

Keywords:

convergence theorem, split common null point problem, Banach space, bounded linear operator.

Abstract

In this paper, we introduce a new iterative scheme for solving the split common null point problem. We then prove the strong convergence theorem under suitable conditions. Finally, we give some numerical examples for our results.

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References

A.S. Alofi, M. Alsulami, W. Takahashi, Strongly convergent iterative method for the split common null point problem in Banach spaces, J. Nonlinear Convex Anal. 2 (2016), 311-324.

Â

M. Alsulami, W. Takahashi, Iterative methods for the split feasibility problem in Banach spaces, J. Convex Anal. 16 (2015), 585-596.

Â

K. Aoyama, Y. Yasunori, W. Takahashi, M. Toyoda, On a strongly nonexpansive sequence in a Hilbert space, J. Nonlinear Convex Anal. 8 (2007), 471-489.

Â

F. E. Browder, Nonlinear maximal monotone operators in Banach spaces, Math. Ann. 175 (1968) 89-113.

https://doi.org/10.1007/BF01418765

Â

C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Prob. 18 (2002), 441-453.

https://doi.org/10.1088/0266-5611/18/2/310

Â

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

Â

B. Halpern, Fixed point of nonexpanding maps, Bull. Amer. Math. Soc. 73(1967), 506-961.

https://doi.org/10.1090/S0002-9904-1967-11864-0

Â

Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in product space, Numer. Algorithms. 8 (1994), 221-239

https://doi.org/10.1007/BF02142692

Â

P.E. Mainge, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal. 16 (2008), 899-912.

https://doi.org/10.1007/s11228-008-0102-z

Â

W. R. Mann, Mean value methods in it iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.

https://doi.org/10.1090/S0002-9939-1953-0054846-3

Â

A. Moudafi, Split monotone variational inclusions, J. Optim. Theory Appl. 150 (2011), 275-283.

https://doi.org/10.1007/s10957-011-9814-6

Â

A. Moudafi, Viscosity approximation method for fixed-points problems, J. Math. Anal. Appl. 241 (2000), 46-55.

https://doi.org/10.1006/jmaa.1999.6615

Â

A. Moudafi, B. S. Thakur, Solving proximal split feasibility problems without prior knowledge of operator norms, Optim. Lett. 8 (2014), 2099-2110.

https://doi.org/10.1007/s11590-013-0708-4

Â

W. Takahashi, Convex Analysis and Approximation of Fixed Point, Yokohama Publishers,Yokohama, 2009.

Â

W. Takahashi, Introduction to Nonlinear and Convex Analysis, Yokohama Publishers, Yokohama, 2009.

Â

W. Takahashi, Nonlinear Functional Analysis, Yokohama, Publishers, Yokohama, 2000.

Â

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

https://doi.org/10.1080/01630563.2013.809360

Â

H. K. Xu, Another control condition in an iterative method for nonexpansive mappings, Bull. Austral. Math. Soc. 65 (2002), 109-113.

https://doi.org/10.1017/S0004972700020116