Geodesic
A composite iterative algorithm for accretive and nonexpansive operators
Zhao, Hengjun1
1 School of Science, Henan University of Engineering, Zhengzhou 451191, China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 6, p. 2957-2965.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.06.10
Classification : 47H06, 47H09, 90C33
Keywords: Accretive operator, nonexpansive operator, uniformly smooth, zero point.

Zhao, Hengjun 1

1 School of Science, Henan University of Engineering, Zhengzhou 451191, China 
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Zhao, Hengjun. A composite iterative algorithm for accretive and nonexpansive operators. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 6, p. 2957-2965. doi : 10.22436/jnsa.010.06.10. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.06.10/

[1] Argyros, I. K.; George, S.; Erappa, S. M. Expanding the applicability of the generalized Newton method for generalized equations, Commun. Optim. Theory, Volume 2017 (2017), pp. 1-12

[2] Dehaish, B. A. Bin; Latif, A.; Bakodah, H. O.; Qin, X.-L. A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces, J. Inequal. Appl., Volume 2015 (2015), pp. 1-14 | DOI | Zbl

[3] Dehaish, B. A. Bin; Qin, X.-L.; Latif, A.; Bakodah, H. O. Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., Volume 16 (2015), pp. 1321-1336 | Zbl

[4] Blum, E.; Oettli, W. From optimization and variational inequalities to equilibrium problems, Math. Student, Volume 63 (1994), pp. 123-145

[5] Browder, F. E. Existence and approximation of solutions of nonlinear variational inequalities, Proc. Nat. Acad. Sci. U.S.A., Volume 56 (1966), pp. 1080-1086 | DOI

[6] Bruck, R. E.; Jr. A strongly convergent iterative solution of \(0 \in U(x)\) for a maximal monotone operator U in Hilbert space, J. Math. Anal. Appl., Volume 48 (1974), pp. 114-126 | Zbl | DOI

[7] Cho, S. Y.; Dehaish, B. A. Bin; Qin, X.-L. Weak convergence of a splitting algorithm in Hilbert spaces, J. Appl. Anal. Comput., Volume 7 (2017), pp. 427-438

[8] Cho, S. Y.; Qin, X.-L.; Wang, L. Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-15 | DOI | Zbl

[9] Combettes, P. L. The convex feasibility problem in image recovery, Adv. Imag. Elect. Phys., Volume 95 (1996), pp. 155-270 | DOI

[10] Combettes, P. L.; R.Wajs, V. Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., Volume 4 (2005), pp. 1168-1200 | DOI | Zbl

[11] Fang, N.-N.; Gong, Y.-P. Viscosity iterative methods for split variational inclusion problems and fixed point problems of a nonexpansive mapping, Commun. Optim. Theory, Volume 2016 (2016), pp. 1-15

[12] Falset, J. García; Kaczor, W.; Kuczumow, T.; Reich, S. Weak convergence theorems for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal., Volume 43 (2001), pp. 377-401 | DOI

[13] Kamimura, S.; Takahashi, W. Approximating solutions of maximal monotone operators in Hilbert spaces, J. Approx. Theory, Volume 106 (2000), pp. 226-240 | DOI

[14] Kato, T. Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, Volume 19 (1967), pp. 508-520 | DOI

[15] Kitahara, S.; Takahashi, W. Image recovery by convex combinations of sunny nonexpansive retractions, Topol. Methods Nonlinear Anal., Volume 2 (1993), pp. 333-342 | Zbl | DOI

[16] Nguyen, N. D.; Buong, N. An iterative method for zeros of accretive mappings in Banach spaces, J. Nonlinear Funct. Anal., Volume 2016 (2016), pp. 1-17

[17] Qin, X.-L.; Cho, S. Y. Convergence analysis of a monotone projection algorithm in reflexive Banach spaces, Acta Math. Sci. Ser. B Engl. Ed., Volume 37 (2017), pp. 488-502 | Zbl | DOI

[18] Qin, X.-L.; Cho, S. Y.; Wang, L. A regularization method for treating zero points of the sum of two monotone operators, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-10 | Zbl | DOI

[19] Qin, X.-L.; Yao, J.-C. Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., Volume 2016 (2016), pp. 1-9 | Zbl | DOI

[20] Reich, S. Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl., Volume 75 (1980), pp. 287-292 | DOI

[21] Rockafellar, R. T. Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Oper. Res., Volume 1 (1976), pp. 97-116 | DOI | Zbl

[22] Takahashi, S.; Takahashi, W.; Toyoda, M. Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces, J. Optim. Theory Appl., Volume 147 (2010), pp. 27-41 | DOI

[23] Xu, H.-K. Inequalities in Banach spaces with applications, Nonlinear Anal., Volume 16 (1991), pp. 1127-1138 | DOI

[24] Zhang, M.-L. Iterative algorithms for common elements in fixed point sets and zero point sets with applications, Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-14 | DOI | Zbl

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