Convergence Theorems for -Nonexpansive Mappings in CAT(0) Spaces

Subject Areas : Applied Mathematics

Savita Rathee ¹ , R. Ritika ²

1 - Department of Mathematics, M.D. University, Rohtak (Haryana), India
2 - Department of Mathematics, M.D. University, Rohtak (Haryana), India

Received: 2015-09-21 Accepted : 2015-09-21 Published : 2015-12-01

Keywords:

Abstract :

In this paper we derive convergence theorems for an -nonexpansive mappingof a nonempty closed and convex subset of a complete CAT(0) space for SP-iterative process and Thianwan's iterative process.

References:

[1] K. Aoyama and F. Kohsaka, Fixed point theorem for -nonexpansive
mappings in Banach spaces, Nonlinear Analysis 74 (2011), 4387-4391.
[2] M. Bridson and A. Hae iger, Metric Spaces of Non-Positive Curvature,
Springer-Verlag, Berlin, Heidelberg, (1999).
[3] F. Bruhat and J. Tits, Groupes reductifs sur un corps local. I. Donnees
radicielles values, Inst. Hautes Etudes Sci. Publ. Math. 41 (1972), 5{251.
[4] S. Dhompongsa, W.A. Kirk and B. Panyanak, Non-expansive set-valued
mappings in metric and Banach spaces, Journal of Nonlinear and Convex
Analysis 8 (2007), 35{45.
[5] S. Dhompongsa, W.A. Kirk and B. Sims, Fixed points of uniformly
lipschitzian mappings, Nonlinear Analysis: TMA 65 (2006), 762{772.
[6] S. Dhompongsa and B. Panyanak, On
-convergence theorems in CAT(0)
spaces, Computer and Mathematics with Applications 56 (2008), 2572{
2579.
[7] W.A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces,
Nonlinear Analysis: TMA 68 (2008), 3689{3696.
[8] T.C. Lim, Remarks on some xed point theorems, Proc. Amer. Math. Soc.
60 (1976), 179{182.

[9] E. Naraghirad, N.C. Wong and J.C. Yao, Approximating xed points
of -nonexpansive mappings in uniformly convex Banach spaces and
CAT(0) spaces, Fixed Point Theory and Applications (2013), 2013:57,
doi:10.1186/1687-1812-2013-57.
[10] W. Phuengrattana and S. Suantai, On the rate of convergence of Mann,
Ishikawa, Noor and SP iterations for continuous functions on an arbitrary
interval, Journal of Computational and Applied Mathematics 235 (2011),
3006{3014.
[11] S. Shabani and S.J.H. Ghoncheh, Approximating xed points
of generalized nonexpansive nonself mappings in CAT(0) spaces,
Mathematics Scientic Journal 7(1) (2011), 89{95.
[12] S. Thianwan, Common xed points of new iterations for two
asymptotically non-expansive non-self mappings in Banach spaces,
Journal of Computational and Applied Mathematics (2009), 688{695.
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