System of N fixed point operator equations with N-pseudo-contractive mapping in reflexive Banach spaces
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Authors
Jinyu Guan
- Department of Mathematics, College of Science, Hebei North University, Zhangjiakou 075000, China.
Yanxia Tang
- Department of Mathematics, College of Science, Hebei North University, Zhangjiakou 075000, China.
Yongchun Xu
- Department of Mathematics, College of Science, Hebei North University, Zhangjiakou 075000, China.
Yongfu Su
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.
Abstract
The purpose of this paper is to study the problem of the system of N fixed point operator equations with N-variables
pseudo-contractive mapping. Firstly, the concept of N-variables pseudo-contractive mapping and relatively concepts of nonlinear
mappings are presented in Banach spaces. Secondly, the existence theorems of solutions for the system of N fixed point operator
equations with N-variables pseudo-contractive mapping are proved in reflexive Banach spaces by using the method of product
spaces. In order to get the expected results, the normalized duality mapping of product Banach spaces is defined. Meanwhile the
reflexivity of the product of reflexive Banach spaces and Opial’s condition of product spaces of Banach spaces are also discussed.
Share and Cite
ISRP Style
Jinyu Guan, Yanxia Tang, Yongchun Xu, Yongfu Su, System of N fixed point operator equations with N-pseudo-contractive mapping in reflexive Banach spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2457--2470
AMA Style
Guan Jinyu, Tang Yanxia, Xu Yongchun, Su Yongfu, System of N fixed point operator equations with N-pseudo-contractive mapping in reflexive Banach spaces. J. Nonlinear Sci. Appl. (2017); 10(5):2457--2470
Chicago/Turabian Style
Guan, Jinyu, Tang, Yanxia, Xu, Yongchun, Su, Yongfu. "System of N fixed point operator equations with N-pseudo-contractive mapping in reflexive Banach spaces." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2457--2470
Keywords
- N-variables pseudo-contractive mapping
- N fixed point
- system of operator equations
- product spaces
- reflexive Banach space
- Opial’s condition.
MSC
References
-
[1]
F. E. Browder, Nonlinear mappings of nonexpansive and accretive type in Banach spaces, Bull. Amer. Math. Soc., (1967), 875–882.
-
[2]
S. S. Chang, Y. J. Cho, B. S. Lee, J. S. Jung, S. M. Kang, Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces, J. Math. Anal. Appl., 224 (1998), 149–165.
-
[3]
Y. J. Cho, S. M. Kang, X.-L. Qin, Some results on k-strictly pseudo-contractive mappings in Hilbert spaces, Nonlinear Anal., 70 (2009), 1956–1964.
-
[4]
K. Deimling, Zeros of accretive operators, Manuscripta Math., 13 (1974), 365–374.
-
[5]
J. García-Falset, E. Llorens-Fuster, Fixed points for pseudocontractive mappings on unbounded domains, Fixed Point Theory Appl., 2010 (2010), 17 pages.
-
[6]
J. García-Falset, S. Reich, Zeroes of accretive operators and the asymptotic behavior of nonlinear semigroups, Houston J. Math., 32 (2006), 1179–1225.
-
[7]
J. S. Jung, Strong convergence of iterative methods for k-strictly pseudo-contractive mappings in Hilbert spaces, Appl. Math. Comput., 215 (2010), 3746–3753.
-
[8]
W. A. Kirk, R. Schöneberg, Zeros of m-accretive operators in Banach spaces, Israel J. Math., 35 (1980), 1–8.
-
[9]
H. Lee, S. Kim, Multivariate coupled fixed point theorems on ordered partial metric spaces, J. Korean Math. Soc., 51 (2014), 1189–1207.
-
[10]
L.-W. Li, W. Song, A hybrid of the extragradient method and proximal point algorithm for inverse strongly monotone operators and maximal monotone operators in Banach spaces, Nonlinear Anal. Hybrid Syst., 1 (2007), 398–413.
-
[11]
C. Morales, Nonlinear equations involving m-accretive operators, J. Math. Anal. Appl., 97 (1983), 329–336.
-
[12]
C. H. Morales, The Leray-Schauder condition for continuous pseudo-contractive mappings, Proc. Amer. Math. Soc., 137 (2009), 1013–1020.
-
[13]
M. Osilike, A. Udomene, Demiclosedness principle and convergence theorems for strictly pseudocontractive mappings of Browder-Petryshyn type, J. Math. Anal. Appl., 256 (2001), 431–445.
-
[14]
N. Petrot, R. Wangkeeree, A general iterative scheme for strict pseudononspreading mapping related to optimization problem in Hilbert spaces, J. Nonlinear Anal. Optim., 2 (2011), 329–336.
-
[15]
Y.-F. Su, A note on ”Convergence of a Halpern-type iteration algorithm for a class of pseudo-contractive mappings”, Nonlinear Anal., 70 (2009), 2519–2520.
-
[16]
Y.-F. Su, M.-Q. Li, New fixed point theorems for pseudocontractive mappings and zero point theorems for accretive operators in Banach spaces, Fixed Point Theory, 11 (2010), 129–132.
-
[17]
Y.-F. Su, A. Petruşel, J.-C. Yao, Multivariate fixed point theorems for contractions and nonexpansive mappings with applications, Fixed Point Theory Appl., 2016 (2016), 19 pages.
-
[18]
W. Takahashi, Nonlinear functional analysis, Fixed point theory and its applications, Yokohama Publishers, Yokohama (2000)
-
[19]
W. Takahashi, Strong convergence theorems for maximal and inverse-strongly monotone mappings in Hilbert spaces and applications, J. Optim. Theory Appl., 157 (2013), 781–802.
-
[20]
Y.-C. Tang, J.-G. Peng, L.-W. Liu, Strong convergence theorem for pseudo-contractive mappings in Hilbert spaces, Nonlinear Anal., 74 (2011), 380–385.
-
[21]
S. Wang, A general iterative method for obtaining an infinite family of strictly pseudo-contractive mappings in Hilbert spaces, Appl. Math. Lett., 24 (2011), 901–907.
-
[22]
Y.-H. Yao, Y.-C. Liou, Y.-P. Chen, Algorithms construction for nonexpansive mappings and inverse-strongly monotone mappings, Taiwanese J. Math., 15 (2011), 1979–1998.
-
[23]
Y.-H. Yao, Y.-C. Liou, G. Marino, A hybrid algorithm for pseudo-contractive mappings, Nonlinear Anal., 71 (2009), 4997–5002.
-
[24]
H. Zhang, Y.-F. Su, Convergence theorems for strict pseudo-contractions in q-uniformly smooth Banach spaces, Nonlinear Anal., 71 (2009), 4572–4580.
-
[25]
H. Zhang, Y.-F. Su, Strong convergence theorems for strict pseudo-contractions in q-uniformly smooth Banach spaces, Nonlinear Anal., 70 (2009), 3236–3242.
-
[26]
H.-Y. Zhou, Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions in Banach spaces, Nonlinear Anal., 68 (2008), 2977–2983.
-
[27]
H.-Y. Zhou, Convergence theorems of fixed points for \(\kappa\)-strict pseudo-contractions in Hilbert spaces, Nonlinear Anal., 69 (2008), 456–462.
-
[28]
H.-Y. Zhou, Y.-F. Su, Strong convergence theorems for a family of quasi-asymptotic pseudo-contractions in Hilbert spaces, Nonlinear Anal., 70 (2009), 4047–4052.