The split common fixed-point problem for demicontractive mappings and quasi-nonexpansive mappings
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 6, p. 2976-2985.

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

In this paper, we study a split common fixed-point problem for demicontractive mappings and quasi-nonexpansive mappings, and propose some cyclic iterative schemes. Moreover we prove some strong convergence theorems. The results obtained in this paper generalize and improve the recent ones announced by many others.
DOI : 10.22436/jnsa.010.06.12
Classification : 47H05, 47H09, 47H20
Keywords: Split common fixed-point problem, demicontractive mapping, strong convergence, cyclic iterative scheme.

Wang, Yaqin 1 ; Kim, Tae-Hwa 2 ; Fang, Xiaoli 1 ; He, Huimin 3

1 Department of Mathematics, Shaoxing University, Shaoxing 312000, China
2 Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan 48513, Korea
3 School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
@article{JNSA_2017_10_6_a11,
     author = {Wang, Yaqin and Kim, Tae-Hwa and Fang, Xiaoli and He, Huimin},
     title = {The split common fixed-point problem for demicontractive mappings and quasi-nonexpansive mappings},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {2976-2985},
     publisher = {mathdoc},
     volume = {10},
     number = {6},
     year = {2017},
     doi = {10.22436/jnsa.010.06.12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.06.12/}
}
TY  - JOUR
AU  - Wang, Yaqin
AU  - Kim, Tae-Hwa
AU  - Fang, Xiaoli
AU  - He, Huimin
TI  - The split common fixed-point problem for demicontractive mappings and quasi-nonexpansive mappings
JO  - Journal of nonlinear sciences and its applications
PY  - 2017
SP  - 2976
EP  - 2985
VL  - 10
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.06.12/
DO  - 10.22436/jnsa.010.06.12
LA  - en
ID  - JNSA_2017_10_6_a11
ER  - 
%0 Journal Article
%A Wang, Yaqin
%A Kim, Tae-Hwa
%A Fang, Xiaoli
%A He, Huimin
%T The split common fixed-point problem for demicontractive mappings and quasi-nonexpansive mappings
%J Journal of nonlinear sciences and its applications
%D 2017
%P 2976-2985
%V 10
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.06.12/
%R 10.22436/jnsa.010.06.12
%G en
%F JNSA_2017_10_6_a11
Wang, Yaqin; Kim, Tae-Hwa; Fang, Xiaoli; He, Huimin. The split common fixed-point problem for demicontractive mappings and quasi-nonexpansive mappings. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 6, p. 2976-2985. doi : 10.22436/jnsa.010.06.12. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.06.12/

[1] Censor, Y.; Elfving, T. A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, Volume 8 (1994), pp. 221-239 | Zbl | DOI

[2] Censor, Y.; Segal, A. The split common fixed point problem for directed operators, J. Convex Anal., Volume 16 (2009), pp. 587-600

[3] Cui, H.-H.; Su, M.-L.; Wang, F.-H. Damped projection method for split common fixed point problems, J. Inequal. Appl., Volume 2013 (2013), pp. 1-10 | DOI | Zbl

[4] Goebel, K.; Kirk, W. A. Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1990 | DOI

[5] Hong, C.-C.; Huang, Y.-Y. A strong convergence algorithm for the two-operator split common fixed point problem in Hilbert spaces, Abstr. Appl. Anal., Volume 2014 (2014), pp. 1-8

[6] Maingé, P. E. Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal., Volume 16 (2008), pp. 899-912 | DOI | Zbl

[7] Marino, G.; Xu, H.-K. Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl., Volume 329 (2007), pp. 336-346 | DOI

[8] Moudafi, A. The split common fixed-point problem for demicontractive mappings, Inverse Problems, Volume 26 (2010), pp. 1-6 | DOI

[9] Wang, Y.-Q.; Kim, T. H. Simultaneous iterative algorithm for the split equality fixed-point problem of demicontractive mappings, J. Nonlinear Sci. Appl., Volume 10 (2017), pp. 154-165 | DOI

[10] Wang, F.-H.; Xu, H.-K. Cyclic algorithms for split feasibility problems in Hilbert spaces, Nonlinear Anal., Volume 74 (2011), pp. 4105-4111 | Zbl | DOI

[11] Xu, H.-K. Iterative algorithms for nonlinear operators, J. London Math. Soc., Volume 66 (2002), pp. 240-256 | DOI

[12] Yao, Y.-H.; Agarwal, R. P.; Postolache, M.; Liou, Y.-C. Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-14 | DOI

[13] Yao, Y.-H.; Postolache, M.; Liou, Y.-C. Strong convergence of a self-adaptive method for the split feasibility problem, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-12 | DOI | Zbl

[14] Yao, Y.-H.; Wu, J.; Liou, Y.-C. Regularized methods for the split feasibility problem, Abstr. Appl. Anal., Volume 2012 (2012), pp. 1-13 | DOI

Cité par Sources :