Demiclosed principals and convergence theorems for asymptotically pseudocontractive nonself-mappings in intermediate sense
-
2108
Downloads
-
3623
Views
Authors
Yunpeng Zhang
- College of Electric Power, North China University of Water Resources and Electric Power, Zhengzhou, 450011, China.
Abstract
In this work, we study fixed points of nonself-mappings which are asymptotically pseudocontractive in the intermediate
sense via an implicit iterative process. Convergence analysis is investigated in the framework of Hilbert spaces. We also give
strong convergence criteria for the class of mappings.
Share and Cite
ISRP Style
Yunpeng Zhang, Demiclosed principals and convergence theorems for asymptotically pseudocontractive nonself-mappings in intermediate sense, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 2229--2240
AMA Style
Zhang Yunpeng, Demiclosed principals and convergence theorems for asymptotically pseudocontractive nonself-mappings in intermediate sense. J. Nonlinear Sci. Appl. (2017); 10(4):2229--2240
Chicago/Turabian Style
Zhang, Yunpeng. "Demiclosed principals and convergence theorems for asymptotically pseudocontractive nonself-mappings in intermediate sense." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 2229--2240
Keywords
- Asymptotically pseducontractive mapping
- implicit algorithm
- metric projection
- convergence analysis.
MSC
References
-
[1]
I. K. Argyros, S. George, On the convergence of inexact Gauss-Newton method for solving singular equations, J. Nonlinear Funct. Anal., 2016 (2016), 22 pages.
-
[2]
B. A. Bin Dehaish, A. Latif, H. O. Bakodah, X.-L. Qin, A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces, J. Inequal. Appl., 2015 (2015), 14 pages.
-
[3]
B. A. Bin Dehaish, X.-L. Qin, A. Latif, H. O. Bakodah, Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321–1336.
-
[4]
F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl., 20 (1967), 197–228.
-
[5]
R. Bruck, T. Kuczumow, S. Reich, Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloq. Math., 65 (1993), 169–179.
-
[6]
S. Y. Cho, B. A. Bin Dehaish, X.-L. Qin, Weak convergence of a splitting algorithm in Hilbert spaces, J. Appl. Anal. Comput., 7 (2017), 427–438.
-
[7]
S. Y. Cho, W.-L. Li, S. M. Kang, Convergence analysis of an iterative algorithm for monotone operators, J. Inequal. Appl., 2013 (2013), 14 pages.
-
[8]
S. Y. Cho, X.-L. Qin, On the strong convergence of an iterative process for asymptotically strict pseudocontractions and equilibrium problems, Appl. Math. Comput., 235 (2014), 430–438.
-
[9]
S. H. Khan, I. Yildirim, M. Ozdemir, Convergence of an implicit algorithm for two families of nonexpansive mappings, Comput. Math. Appl., 59 (2010), 3084–3091.
-
[10]
J. K. Kim, S. Y. Cho, X.-L. Qin, Some results on generalized equilibrium problems involving strictly pseudocontractive mappings, Acta Math. Sci. Ser. B Engl. Ed., 31 (2011), 2041–2057.
-
[11]
J. K. Kim, Y. M. Nam, J. Y. Sim, Convergence theorems of implicit iterative sequences for a finite family of asymptotically quasi-nonxpansive type mappings, Nonlinear Anal., 71 (2009), e2839–e2848.
-
[12]
W. A. Kirk, Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math., 17 (1974), 339–346.
-
[13]
Q.-H. Liu, Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings, Nonlinear Anal., 26 (1996), 1835–1842.
-
[14]
S.-T. Lv, Implicit algorithms for a demicontinuous semigroup of pseudocontractions, Commun. Optim. Theory, 2017 (2017), 9 pages.
-
[15]
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), 591–597.
-
[16]
M. O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl., 294 (2004), 73–81.
-
[17]
M. O. Osilike, B. G. Akuchu, Common fixed points of a finite family of asymptotically pseudocontractive maps, Fixed Point Theory Appl., 2004 (2004), 81–88.
-
[18]
X.-L. Qin, S. Y. Cho, Convergence analysis of a monotone projection algorithm in reflexive Banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 37 (2017), 488–502.
-
[19]
X.-L. Qin, S. Y. Cho, L. Wang, A regularization method for treating zero points of the sum of two monotone operators, Fixed Point Theory Appl., 2014 (2014), 10 pages.
-
[20]
X.-L. Qin, J.-C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 9 pages.
-
[21]
J. Reinermann, Über Fixpunkte kontrahierender Abbildungen und schwach konvergente Toeplitz-Verfahren, (German) Arch. Math. (Basel), 20 (1969), 59–64.
-
[22]
D. R. Sahu, H.-K. Xu, J.-C. Yao, Asymptotically strict pseudocontractive mappings in the intermediate sense, Nonlinear Anal., 70 (2009), 3502–3511.
-
[23]
J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 158 (1991), 407–413.
-
[24]
T. V. Su, T. V. Dinh, On the existence of solutions of quasi-equilibrium problems (UPQEP), (LPQEP), (UWQEP) and (LWQEP) and related problems, Commun. Optim. Theory, 2016 (2016), 21 pages.
-
[25]
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.
-
[26]
Z.-M. Wang, Implicit hybrid projection algorithms for common fixed points of a demicontinuous semigroup of pseudocontractions in Hilbert spaces, J. Nonlinear Funct. Anal., 2015 (2015), 12 pages.
-
[27]
H.-Y. Zhou, Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces, Nonlinear Anal., 70 (2009), 3140–3145.