Weak convergence of an iterative algorithm for accretive operators
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 8, p. 4099-4108.

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

In this paper, an iterative algorithm investigated for $m$-accretive and inverse-strongly accretive operators. Also, a weak convergence theorem for the sum of two accretive operators is established in a real uniformly convex and $q$-uniformly smooth Banach space.
DOI : 10.22436/jnsa.010.08.06
Classification : 47H06, 90C33
Keywords: Accretive operator, zero point, projection, splitting method, weak convergence.

Zhao, Hengjun 1 ; Cho, Sun Young 2

1 School of Science, Henan University of Engineering, Zhengzhou 451191, China
2 Center for General Education, China Medical University, Taichung, Taiwan
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Zhao, Hengjun; Cho, Sun Young. Weak convergence of an iterative algorithm for accretive operators. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 8, p. 4099-4108. doi : 10.22436/jnsa.010.08.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.08.06/

[1] Alspach, D. E. A fixed point free nonexpansive map , Proc. Amer. Math. Soc., Volume 82 (1981), pp. 423-424 | DOI

[2] Argyros, I. K.; S. George On the convergence of inexact Gauss-Newton method for solving singular equations, J. Nonlinear Funct. Anal., Volume 2016 (2016), pp. 1-22

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

[4] Dehaish, B. A. Bin; Qin, X.-L.; Latif, A.; H. O. Bakodah 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

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

[6] Browder, F. E. Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A., Volume 54 (1965), pp. 1041-1044 | DOI

[7] Bruck, R. E. A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, Israel J. Math., Volume 32 (1979), pp. 107-116 | DOI | Zbl

[8] Byrne, C. A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, Volume 20 (2004), pp. 103-120 | Zbl | DOI

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

[10] Cho, S. Y.; Kang, S. M. Approximation of common solutions of variational inequalities via strict pseudocontractions, Acta Math. Sci. Ser. B Engl. Ed., Volume 32 (2012), pp. 1607-1618 | Zbl | DOI

[11] Cho, S. Y.; Li, W.-L.; Kang, S. M. Convergence analysis of an iterative algorithm for monotone operators, J. Inequal. Appl., Volume 2013 (2013), pp. 1-14 | DOI

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

[13] Han, S.-P.; G. Lou A parallel algorithm for a class of convex programs, SIAM J. Control Optim., Volume 26 (1988), pp. 345-355 | DOI

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

[15] S.-T. Lv Convergence analysis of a Halpern-type iterative algorithm for zero points of accretive operators, Commun. Optim. Theory, Volume 2016 (2016), pp. 1-9

[16] Martinet, B. Régularisation d’inéquations variationnelles par approximations successives, (French) Rev. Française Informat. Recherche Opérationnelle, Volume 4 (1970), pp. 154-158 | Zbl

[17] B. Martinet Détermination approchée d’un point fixe d’une application pseudo-contractante , Cas de l’application prox, (French) C. R. Acad. Sci. Paris Sér. A-B, Volume 274 (1972), pp. 163-165 | Zbl

[18] G. B. Passty Ergodic convergence to a zero of the sum of monotone operators in Hilbert space, J. Math. Anal. Appl., Volume 72 (1979), pp. 383-390 | DOI

[19] Qin, X.-L.; Chang, S.-S.; Y. J. Cho Iterative methods for generalized equilibrium problems and fixed point problems with applications, Nonlinear Anal. Real World Appl., Volume 11 (2010), pp. 2963-2972 | DOI

[20] Qin, X.-L.; S. Y. Cho 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

[21] 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 | DOI

[22] 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

[23] R. T. Rockafellar Monotone operators and the proximal point algorithm, SIAM J. Control Optimization, Volume 14 (1976), pp. 877-898 | DOI

[24] Sahu, D. R.; Yao, J. C. A generalized hybrid steepest descent method and applications, J. Nonlinear Var. Anal., Volume 1 (2017), pp. 111-126

[25] W. Takahashi Weak and strong convergence theorems for families of nonlinear and nonself mappings in Hilbert spaces, J. Nonlinear Var. Anal., Volume 1 (2017), pp. 1-23

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

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

[28] Yang, S. Zero theorems of accretive operators in reflexive Banach spaces, J. Nonlinear Funct. Anal., Volume 2013 (2013), pp. 1-12

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