A composite iterative algorithm for accretive and nonexpansive operators
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Authors
Hengjun Zhao
- School of Science, Henan University of Engineering, Zhengzhou 451191, China.
Abstract
In this paper, we propose a one-step composite iterative algorithm for solving operator equations involving accretive and
nonexpansive operators. We obtain a weak convergence theorem for these nonlinear operators in the framework of 2-uniformly
smooth and uniformly convex Banach space.
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ISRP Style
Hengjun Zhao, A composite iterative algorithm for accretive and nonexpansive operators, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 6, 2957--2965
AMA Style
Zhao Hengjun, A composite iterative algorithm for accretive and nonexpansive operators. J. Nonlinear Sci. Appl. (2017); 10(6):2957--2965
Chicago/Turabian Style
Zhao, Hengjun. "A composite iterative algorithm for accretive and nonexpansive operators." Journal of Nonlinear Sciences and Applications, 10, no. 6 (2017): 2957--2965
Keywords
- Accretive operator
- nonexpansive operator
- uniformly smooth
- zero point.
MSC
References
-
[1]
I. K. Argyros, S. George, S. M. Erappa, Expanding the applicability of the generalized Newton method for generalized equations, Commun. Optim. Theory, 2017 (2017), 12 pages.
-
[2]
B. A. Bin Dehaish, A. Latif, H. O. Bakodah, X.-L. Qin, A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces, J. Inequal. Appl., 2015 (2015), 14 pages.
-
[3]
B. A. Bin Dehaish, X.-L. Qin, A. Latif, H. O. Bakodah, Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321–1336.
-
[4]
E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123–145.
-
[5]
F. E. Browder, Existence and approximation of solutions of nonlinear variational inequalities, Proc. Nat. Acad. Sci. U.S.A., 56 (1966), 1080–1086.
-
[6]
R. E. Bruck, Jr., A strongly convergent iterative solution of \(0 \in U(x)\) for a maximal monotone operator U in Hilbert space, J. Math. Anal. Appl., 48 (1974), 114–126.
-
[7]
S. Y. Cho, B. A. Bin Dehaish, X.-L. Qin, Weak convergence of a splitting algorithm in Hilbert spaces, J. Appl. Anal. Comput., 7 (2017), 427–438.
-
[8]
S. Y. Cho, X.-L. Qin, L. Wang, Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory Appl., 2014 (2014), 15 pages.
-
[9]
P. L. Combettes, The convex feasibility problem in image recovery, Adv. Imag. Elect. Phys., 95 (1996), 155–270.
-
[10]
P. L. Combettes, V. R.Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), 1168–1200.
-
[11]
N.-N. Fang, Y.-P. Gong, Viscosity iterative methods for split variational inclusion problems and fixed point problems of a nonexpansive mapping, Commun. Optim. Theory, 2016 (2016), 15 pages.
-
[12]
J. García Falset, W. Kaczor, T. Kuczumow, S. Reich, Weak convergence theorems for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal., 43 (2001), 377–401.
-
[13]
S. Kamimura, W. Takahashi, Approximating solutions of maximal monotone operators in Hilbert spaces, J. Approx. Theory, 106 (2000), 226–240.
-
[14]
T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 508–520.
-
[15]
S. Kitahara, W. Takahashi, Image recovery by convex combinations of sunny nonexpansive retractions, Topol. Methods Nonlinear Anal., 2 (1993), 333–342.
-
[16]
N. D. Nguyen, N. Buong, An iterative method for zeros of accretive mappings in Banach spaces, J. Nonlinear Funct. Anal., 2016 (2016), 17 pages.
-
[17]
X.-L. Qin, S. Y. Cho, Convergence analysis of a monotone projection algorithm in reflexive Banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 37 (2017), 488–502.
-
[18]
X.-L. Qin, S. Y. Cho, L. Wang, A regularization method for treating zero points of the sum of two monotone operators, Fixed Point Theory Appl., 2014 (2014), 10 pages.
-
[19]
X.-L. Qin, J.-C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 9 pages.
-
[20]
S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl., 75 (1980), 287–292.
-
[21]
R. T. Rockafellar, Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Oper. Res., 1 (1976), 97–116.
-
[22]
S. Takahashi, W. Takahashi, M. Toyoda, Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces, J. Optim. Theory Appl., 147 (2010), 27–41.
-
[23]
H.-K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal., 16 (1991), 1127–1138.
-
[24]
M.-L. Zhang, Iterative algorithms for common elements in fixed point sets and zero point sets with applications, Fixed Point Theory Appl., 2012 (2012), 14 pages.
