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http://dx.doi.org/10.4134/CKMS.c160005

CONVERGENCE OF A NEW MULTISTEP ITERATION IN CONVEX CONE METRIC SPACES  

Gunduz, Birol (Department of Mathematics Faculty of Science and Art Erzincan University)
Publication Information
Communications of the Korean Mathematical Society / v.32, no.1, 2017 , pp. 39-46 More about this Journal
Abstract
In this paper, we propose a new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex cone metric spaces. Then we show that our iteration converges to a common fixed point of this class of mappings under suitable conditions. Our result generalizes the corresponding result of Lee [5] from the closed convex subset of a convex cone metric space to whole space.
Keywords
convex metric spaces; cone metric spaces; asymptotically quasi-nonexpansive mappings; common fixed point; strong convergence;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 B. Gunduz, A new multistep iteration for a finite family of asymptotically quasinonexpansive mappings in convex metric spaces, J. Nonlinear Sci. Appl. 9 (2016), no. 3, 1365-1372.   DOI
2 L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 322 (2007), no. 2, 1468-1476.
3 A. R. Khan and M. A. Ahmed, Convergence of a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications, Comput. Math. Appl. 59 (2010), no. 8, 2990-2995.   DOI
4 B. S. Lee, Approximating common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex cone metric spaces, Univ. J. Appl. Math. 1 (2013), no. 3, 166-171.
5 B. S. Lee, Strong convergence in noor-type iterative schemes in convex cone metric spaces, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 22 (2015), no. 2, 185-197.
6 L. A. Talman, Fixed points for condensing multifunctions in metric spaces with convex structure, Kodai Math. Sem. Rep. 29 (1977), no. 1-2, 62-70.   DOI
7 Q. Liu, Iterative sequence for asymptotically quasi-nonexpansive mappings with errors member, J. Math. Anal. Appl. 259 (2001), no. 1, 18-24.   DOI
8 S. Suantai, Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 311 (2005), no. 2, 506-517.   DOI
9 W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai. Math. Sem. Rep. 22 (1970), 142-149.   DOI
10 B. L. Xu and M. A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002), no. 2, 444-453.   DOI
11 L. Yang, Modified multistep iterative process for some common fixed point of a finite family of nonself asymptotically nonexpansive mappings, Math. Comput. Modelling 45 (2007), no. 9-10, 1157-1169.   DOI