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http://dx.doi.org/10.7858/eamj.2017.002

EQUIVALENCE BETWEEN SOME ITERATIVE SCHEMES FOR GENERALIZED φ-WEAK CONTRACTION MAPPING IN CAT(0) SPACES  

Kim, Kyung Soo (Graduate School of Education, Mathematics Education Kyungnam University)
Publication Information
East Asian mathematical journal / v.33, no.1, 2017 , pp. 11-22 More about this Journal
Abstract
The aim of this paper is to obtain equivalence of convergence between some iterative schemes for generalized ${\varphi}$-weak contraction mapping in CAT(0) spaces.
Keywords
CAT(0) space; generalized ${\varphi}$-weak contraction; fixed point; iterative scheme;
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1 Y. I. Alber, and S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, in: I. Gohberg, Yu. Lyubich(Eds.), New Results in Operator Theory, in: Advances and Appl., vol. 98, Birkhauser, Basel, 1997, 7-22.
2 V. Berinde, Iterative approximation of fixed points, Jour efemeride, Bala Mare, 2002.
3 F. Bruhat, and J. Tits, Groups reductifss sur un corps local. I. Donnees radicielles valuees, Publ. Math. Inst. Hautes Etudes Sci. 41 (1972), 5-251.   DOI
4 M. Bridson, and A. Haefliger, Metric spaces of Non-Positive Curvature, Springer-Verlag, Berlin, Heidelberg, 1999.
5 D. Burago, Y. Burago, and S. Ivanov, A course in metric Geometry, in:Graduate studies in Math., 33, Amer. Math. Soc., Providence, Rhode Island, 2001.
6 P. Chaoha, and A. Phon-on, A note on fixed point sets in CAT(0) spaces, J. Math. Anal. Appl. 320 (2006), 983-987.   DOI
7 S. Dhompongsa, and B. Panyanak, On triangle-convergence theorems in CAT(0) spaces, Comput. Math. Anal. 56 (2008), 2572-2579.
8 R. Espnola, and B. Piatek, The fixed point property and unbounded sets in CAT(0) spaces, J. Math. Anal. Appl. 408 (2013), 638-654.   DOI
9 M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ. 8. Springer, New York, 1987.
10 S. Ishikawa, Fixed point by a new iteration, Proc. Amer. Math. Soc. 44 (1974), 147-150.   DOI
11 J. K. Kim, K. H. Kim, and K. S. Kim, Three-step iterative sequences with errors for asymptotically quasi-nonexpansive mappings in convex metric spaces, Proc. of RIMS Kokyuroku, Kyoto Univ. 1365 (2004), 156-165.
12 J. K. Kim, K. H. Kim, and K. S. Kim, Convergence theorems of modified three-step iterative sequences with mixed errors for asymptotically quasi-nonexpansive mappings in Banach spaces, PanAmerican Math. Jour. 14 (2004), no. 1, 45-54.
13 J. K. Kim, K. S. Kim, and Y. M. Nam, Convergence and stability of iterative processes for a pair of simultaneously asymptotically quasi-nonexpansive type mappings in convex metric spaces, J. of Compu. Anal. Appl. 9 (2007), no. 2, 159-172.
14 K. S. Kim, Some convergence theorems for contractive type mappings in CAT(0) spaces, Abst. Appl. Anal., Vol. 2013, Article ID 381715, 9 pages.
15 E. Picard, Sur les groupes de transformation des equations differentielles lineaires, Comptes Rendus Acad. Sci. Paris 96 (1883), 1131-1134.
16 W. A. Kirk, A fixed point theorem in CAT(0) spaces and ${\mathbb{R}}$-trees, Fixed Point Theory Appl. 2004 (2004), no. 4, 309-316.
17 U. Kohlenbach, and L. Leustean, Mann iterates of directionally nonexpansive mappings in hyperbolic spaces, Abst. Appl. Anal. 2003 (2003), no. 8, 449-477.   DOI
18 L. Leustean, A quadratic rate of asymptotic regularity for CAT(0)-spaces, J. Math. Anal. Appl. 325 (2007), 386-399.   DOI
19 B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001), 2683-2693.   DOI
20 S. Saejung, Halpern's iteration in CAT(0) spaces, Fixed Point Theory Appl. 2010, Article ID 471781, 13 pages.
21 W. Takahashi, A convexity in metric spaces and nonexpansive mappings, Kodai Math. Sem. Rep. 22 (1970), 142-149.   DOI
22 Z. Xue, The convergence of fixed point for a kind of weak contraction, Nonlinear Func. Anal. Appl. 21 (2016), no. 3, 497-500.
23 W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.   DOI