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FIXED POINTS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE IN CAT(0) SPACES
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 Title & Authors
FIXED POINTS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE IN CAT(0) SPACES
Abbas, Mujahid; Thakur, Balwant Singh; Thakur, Dipti;
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 Abstract
The purpose of this paper is to investigate the demiclosed principle, the existence theorems and convergence theorems in CAT(0) spaces for a class of mappings which is essentially wider than that of asymptotically nonexpansive mappings. The structure of fixed point set of such mappings is also studied. Our results generalize, unify and extend several comparable results in the existing literature.
 Keywords
CAT(0) space;asymptotically nonexpansive mapping in the intermediate sense;demiclosed principle;-convergence;iterative approximation;strong convergence;common fixed point;
 Language
English
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 References
1.
R. P. Agarwal, D. O'Regan, and D. R. Sahu, Fixed point theory for Lipschitzian-type mappings with applications, Topological Fixed Point Theory and Its Applications 6, Springer, New York, 2009.

2.
M. Bridson and A. Haeflinger, Metric Spaces of Non-positive Curvature, Springer-Verlag, Berlin, 1999.

3.
F. E. Browder, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660-665. crossref(new window)

4.
R. E. Bruck, Y. Kuczumow, and S. Reich, Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloq. Math. 65 (1993), no. 2, 169-179.

5.
F. Bruhat and J. Tits, Groupes reductifs sur un corps local, Inst. Hautes etudes Sci. Publ. Math. 41 (1972), 5-251. crossref(new window)

6.
D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry, in: Graduate Studies in Mathematics, Vol. 33, Americal Mathematical Society, Providence, RI, 2001.

7.
S. S. Chang, K. K. Tan, H. W. J. Lee, and C. K. Chan, On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 313 (2006), no. 1, 273-283. crossref(new window)

8.
C. E. Chidume and N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62 (2005), no. 6, 1149-1156. crossref(new window)

9.
S. Dhompongsa, W. A. Kirk, and B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal. 8 (2007), no. 1, 35-45.

10.
S. Dhompongsa, W. A. Kirk, and B. Sims, Fixed points of uniformly lipschitzian mappings, Nonlinear Anal. 65 (2006), no. 4, 762-772. crossref(new window)

11.
S. Dhompongsa and B. Panyanak, On ${\Delta}$-convergence theorem in CAT(0) spaces, Comput. Math. Appl. 56 (2008), no. 10, 2572-2579. crossref(new window)

12.
R. Espinola and A. Nicolae, Geodesic Ptolemy spaces and fixed points, Nonlinear Anal. 74 (2011), no. 1, 27-34. crossref(new window)

13.
H. Fukhar-ud-din and S. H. Khan, Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications, J. Math. Anal. Appl. 328 (2007), no. 2, 821-829. crossref(new window)

14.
K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171-174. crossref(new window)

15.
K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990.

16.
K. Goebel and S. Reich, Uniform convexity, hyperbolic geometry, and nonexpansive mappings, Marcel Dekker, Inc., New York, 1984.

17.
N. Hussain and M. A. Khamsi, On asymptotic pointwise contractions in metric spaces, Nonlinear Anal. 71 (2009), no. 10, 4423-4429. crossref(new window)

18.
W. A. Kirk, Geodesic geometry and fixed point theory, in Seminar of Mathematical Analysis (Malaga/Seville, 2002/2003), Vol.64, Coleccion Abierta, pp.195-225, University de Sevilla, Secretariado de Publicaciones, Sevilla, Spain, 2003.

19.
W. A. Kirk, Geodesic geometry and fixed point theory II, in International Conference on Fixed Point Theory and Applications, pp. 113-142, Yokohama Publishers, Yokohama, Japan, 2004.

20.
W. A. Kirk, Fixed point theorems in CAT(0) spaces and ${\mathbb{Z}}$-trees, Fixed Point Theory Appl. 2004 (2004), no. 4, 309-316.

21.
W. A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. 68 (2008), no. 12, 3689-3696. crossref(new window)

22.
T. C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60 (1976), 179-182. crossref(new window)

23.
B. Nanjaras and B. Panyanak, Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. 2010 (2010), Art. ID 268780, 14 pp.

24.
D. R. Sahu and I. Beg, Weak and strong convergence for fixed points of nearly asymptotically non-expansive mappings, Int. J. Mod. Math. 3 (2008), no. 2, 135-151.

25.
H. F. Senter and W. G. Dotson, Jr., Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974), 375-380. crossref(new window)

26.
N. Shahzad and H. Zegeye, Strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi-nonexpansive maps, Appl. Math. Comput. 189 (2007), no. 2, 1058-1065. crossref(new window)

27.
Z. H. Sun, Strong Convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003), no. 1, 351-358. crossref(new window)

28.
K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), no. 2, 301-308. crossref(new window)

29.
H. K. Xu, Existence and convergence for fixed points of mappings of asymptotically nonexpansive type, Nonlinear Anal. 16 (1991), no. 12, 1139-1146. crossref(new window)

30.
H. K. Xu and R. G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001), no. 5-6, 767-773. crossref(new window)