Convergence theorems and stability results of pointwise asymptotically nonexpansive mapping in Banach space
-
2627
Downloads
-
5226
Views
Authors
Qiansheng Feng
- Department of Mathematics, Tianjin University, Tianjin, 300354, China.
Nan Jiang
- Department of Mathematics, Tianjin University, Tianjin, 300354, China.
Yongfu Su
- Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China.
Abstract
The purpose of this paper is to approximate
the fixed point of pointwise asymptotically nonexpansive mapping
using the generalized Mann and generalized Ishikawa iterative scheme.
And under the condition that the pointwise asymptotically nonexpansive
mapping is compact, the stability results of the two iterative schemes
are studied.
The main results of this paper modify and improve many important recent
results in the literature.
Share and Cite
ISRP Style
Qiansheng Feng, Nan Jiang, Yongfu Su, Convergence theorems and stability results of pointwise asymptotically nonexpansive mapping in Banach space, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 10, 5165--5173
AMA Style
Feng Qiansheng, Jiang Nan, Su Yongfu, Convergence theorems and stability results of pointwise asymptotically nonexpansive mapping in Banach space. J. Nonlinear Sci. Appl. (2017); 10(10):5165--5173
Chicago/Turabian Style
Feng, Qiansheng, Jiang, Nan, Su, Yongfu. "Convergence theorems and stability results of pointwise asymptotically nonexpansive mapping in Banach space." Journal of Nonlinear Sciences and Applications, 10, no. 10 (2017): 5165--5173
Keywords
- Pointwise asymptotically nonexpansive mapping
- generalized Mann iterative scheme
- generalized Ishikawa iterative scheme
- stability result
- convergence theorem
MSC
References
-
[1]
I. D. Arandjelović, Note on asymptotic contractions , Appl. Anal. Discrete Math., 1 (2007), 211–216.
-
[2]
J. Balooee, Weak and strong convergence theorems of modified Ishikawa iteration for an infinitely countable family of pointwise asymptotically nonexpansive mappings in Hilbert spaces, Arab J. Math. Sci., 17 (2011), 153–169.
-
[3]
A. O. Bosede, B. E. Rhoades, Stability of Picard and Mann iteration for a general class of functions, J. Adv. Math. Stud., 3 (2010), 23–25.
-
[4]
H. Dehghan, Demiclosed principle and convergence of a hybrid algorithm for multivalued *-nonexpansive mappings, Fixed Point Theory, 14 (2013), 107–115.
-
[5]
K. Goebel, W. A. Kirk , A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171–174.
-
[6]
A. M. Harder, T. L. Hicks, Stability results for fixed point iteration procedures, Math. Japon., 33 (1988), 693–706.
-
[7]
G. Khalilzadeh, R. Sarikhani, Fixed Point for pointwise asymptotically nonexpansive mapping in Banach Space which has Frechet Differential Norm, Int. J. Math. Anal., 7 (2013), 425–432.
-
[8]
W. A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl., 277 (2003), 645–650.
-
[9]
W. A. Kirk , Asymptotic pointwise contractions, Plenary Lecture, the 8th International Conference on Fixed Point Theory and Its Applications, Chiang Mai University, Thailand, (2007), 16–22.
-
[10]
W. A. Kirk, H.-K. Xu, Asymptotic pointwise contractions, Nonlinear Anal., 69 (2008), 4706–4712.
-
[11]
W. M. Kozlowski , Fixed point iteration processes for asymptotic pointwise nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 377 (2011), 43–52.
-
[12]
Z. Ma, L. Wang, Demiclosed principle and convergence theorems for asymptotically strictly pseudononspreading mappings and mixed equilibrium problems, Fixed Point Theory Appl., 2014 (2014), 20 pages.
-
[13]
Z. Opial , Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), 591–597.
-
[14]
S. Rezapour, R. H. Haghi, B. E. Rhoades, Some results about T-stability and almost T-stability, Fixed Point Theory, 12 (2011), 179–186.
-
[15]
B. E. Rhoades, Fixed point theorems and stability results for fixed point iteration procedures, Indian J. Pure Appl. Math., 21 (1990), 1–9.
-
[16]
J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc., 43 (1991), 153–159.
-
[17]
K.-K. Tan, H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178 (1993), 301–308.
-
[18]
R.Wangkeeree, H. Dehghan , Strong and-convergence of Moudafi’s iterative scheme in CAT(0) spaces, J. Nonlinear Conv. Anal., 16 (2015), 299-309.
-
[19]
H.-K. Xu, Asymptotic and weakly asymptotic contractions, Indian J. Pure Appl. Math., 36 (2005), 145–150.
-
[20]
Q. Yuan, B. E. Rhoades, T-Stability of Picard Iteration in Metric Spaces, Fixed Point Theory and Appl., 2008 (2008), 4 pages.
-
[21]
T. Zamfirescu, Fix point theorems in metric spaces, Arch. Math., 23 (1972), 292–298.