Geodesic
Iterative methods for fixed point problems and generalized split feasibility problems in Banach spaces
Song, Yanlai 1
1 College of Science, Zhongyuan University of Technology, 450007 Zhengzhou, China
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 2, p. 198-217.

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

In this paper, we study the Halpern type iterative algorithm to approximate a common solution of fixed point problems of an infinite family of demimetric mappings and generalized split feasibility problems with firmly nonexpansive-like mappings in Banach spaces. We also prove strong convergence theorems for a common solution of the above-said problems by the proposed iterative algorithm and discuss some applications of our results. The methods in this paper are novel and different from those given in many other paper. And the results are the extension and improvement of the recent results in the literature.
DOI : 10.22436/jnsa.011.02.03
Classification : 47H09, 47H10, 49H17
Keywords: Banach space, generalized split feasibility problem, fixed point, metric resolvent, demimetric mapping

Song, Yanlai  1

1 College of Science, Zhongyuan University of Technology, 450007 Zhengzhou, China 
@article{JNSA_2018_11_2_a2,
     author = {Song, Yanlai },
     title = {Iterative methods for fixed point problems and generalized split feasibility problems  in {Banach} spaces},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {198-217},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2018},
     doi = {10.22436/jnsa.011.02.03},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.02.03/}
}
TY  - JOUR
AU  - Song, Yanlai 
TI  - Iterative methods for fixed point problems and generalized split feasibility problems  in Banach spaces
JO  - Journal of nonlinear sciences and its applications
PY  - 2018
SP  - 198
EP  - 217
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.02.03/
DO  - 10.22436/jnsa.011.02.03
LA  - en
ID  - JNSA_2018_11_2_a2
ER  - 
%0 Journal Article
%A Song, Yanlai 
%T Iterative methods for fixed point problems and generalized split feasibility problems  in Banach spaces
%J Journal of nonlinear sciences and its applications
%D 2018
%P 198-217
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.02.03/
%R 10.22436/jnsa.011.02.03
%G en
%F JNSA_2018_11_2_a2
Song, Yanlai . Iterative methods for fixed point problems and generalized split feasibility problems  in Banach spaces. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 2, p. 198-217. doi : 10.22436/jnsa.011.02.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.02.03/

[1] Akashi, S.; W. Takahashi Weak convergence theorem for an infinite family of demimetric mappings in a Hilbert space, J. Nonlinear Convex Anal., Volume 10 (2016), pp. 2159-2169 | Zbl

[2] Aoyama, K.; F. Kohsaka Existence of fixed points of firmly nonexpansive-like mappings in Banach spaces, Fixed Point Theory Appl., Volume 2010 (2010), pp. 1-15 | Zbl | DOI

[3] Aoyama, K.; Kohsaka, F.; W. Takahashi Strong convergence theorems for a family of mappings of type (P) and applications, Nonlinear Anal. Optim., Volume 2009 (2009), pp. 1-17

[4] Aoyama, K.; Kohsaka, F.; W. Takahashi Three generalizations of firmly nonexpansive mappings: their relations and continuous properties, J. Nonlinear Convex Anal., Volume 10 (2009), pp. 131-147

[5] Browder, F. E. Nonlinear maximal monotone operators in Banach spaces, Math. Ann., Volume 175 (1968), pp. 89-113 | DOI

[6] Byrne, C. Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Probl., Volume 18 (2002), pp. 441-453 | Zbl | DOI

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

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

[9] Chang, S. S.; Wang, L.; Y. Zhao On a class of split equality fixed point problems in Hilbert spaces, J. Nonlinear Var. Anal., Volume 1 (2017), pp. 201-212

[10] Chidume, C.; Ş. Măruşter Iterative methods for the computation of fixed points of demicontractive mappings, J. Comput. Appl. Math., Volume 234 (2010), pp. 861-882 | Zbl | DOI

[11] S. Y. Cho Strong convergence analysis of a hybrid algorithm for nonlinear operators in a Banach space, J. Appl. Anal. Comput., Volume 8 (2018), pp. 19-31

[12] Hojo, M.; Takahashi, W.; I. Termwuttipong Strong convergence theorems for 2-generalized hybrid mappings in Hilbert spaces , Nonlinear Anal., Volume 75 (2012), pp. 2166-2176 | DOI | Zbl

[13] Kocourek, P.; Takahashi, W.; Yao, J.-C. Fixed point theorems and weak convergence theorems for generalized hybrid mappings in Hilbert spaces, Taiwanese J. Math., Volume 14 (2010), pp. 2497-2511 | DOI

[14] Maingé, P. E. Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., Volume 325 (2007), pp. 469-479 | DOI

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

[16] Matsushita, S.; Takahashi, W. Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces, Fixed Point Theory Appl., Volume 2004 (2004), pp. 1-10 | DOI

[17] Naraghirad, E.; L. J. Lin Strong convergence theorems for generalized nonexpansive mappings on star-shaped set with applications , Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-24 | DOI | Zbl

[18] Qin, X.; Yao, J.-C. Projection splitting algorithm for nonself operator, J. Nonlinear Convex Anal., Volume 18 (2017), pp. 925-935

[19] Rockafellar, R. T. Characterization of the subdifferentials of convex functions, Pacific J. Math., Volume 17 (1966), pp. 497-510

[20] Rockafellar, R. T. On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc., Volume 149 (1970), pp. 75-88 | 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] Shehu, Y.; Iyiola, O. S.; C. D. Enyi An iterative algorithm for solving split feasibility problems and fixed point problems in Banach spaces , Numer. Algorithms, Volume 72 (2016), pp. 835-864 | Zbl | DOI

[23] Takahashi, W. Convex Analysis and Approximation of Fixed Points, Yokohama Publishers, Yokohama, 2000

[24] W. Takahashi Nonlinear Functional Analysis, Yokohama Publ., Yokohama, 2000

[25] Takahashi, S.; W. Takahashi The split common null point problem and the shrinking projection method in Banach spaces, Optimization, Volume 65 (2016), pp. 281-287 | DOI

[26] 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

[27] Takahashi, W.; J.-C. Yao Strong convergence theorems by hybrid methods for the split common null point problem in Banach spaces, Fixed Point Theory Appl., Volume 2015 (2015), pp. 1-13 | DOI | Zbl

[28] Tan, K.-K.; Xu, H.-K. Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., Volume 178 (1993), pp. 301-308 | DOI

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

[30] Y.-H.Yao; Zhou, H.-Y.; Y.-C. Liou Weak and strong convergence theorems for an asymptotically k-strict pseudo-contraction and a mixed equilibrium problem, J. Korean Math. Soc., Volume 46 (2009), pp. 561-576 | DOI | Zbl

[31] Yu, Z.-T.; Lin, L.-J.; C.-S. Chuang Mathematical programming with multiple sets split monotone variational inclusion constraints, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-27 | DOI | Zbl

Cité par Sources :