Some Convergence Results for Multi-valued Mappings in Hyperbolic Spaces

Abstract In this paper, we modify the iteration process of Agarwal et al. (J. Nonlinear Convex Anal. 8(1) (2007), 61–79) to three multi-valued mappings and prove the strong and △-convergence theorems of this iteration in a hyperbolic space. Our theorems extend and improve some recent results announced in the current literature.

[1]  Ulrich Kohlenbach,et al.  Some logical metatheorems with applications in functional analysis , 2003 .

[2]  W. Takahashi,et al.  Fixed points of multivalued mappings in certain convex metric spaces , 1996 .

[3]  Itai Shafrir,et al.  Nonexpansive iterations in hyperbolic spaces , 1990 .

[4]  Habtu Zegeye,et al.  On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces , 2009 .

[5]  S. Ishikawa Fixed points by a new iteration method , 1974 .

[6]  Teck-Cheong Lim,et al.  Remarks on some fixed point theorems , 1976 .

[7]  H. Busemann Spaces with non-positive curvature , 1948 .

[8]  Yeol Je Cho,et al.  SOME NOTES ON ISHIKAWA ITERATION FOR MULTI-VALUED MAPPINGS , 2011 .

[9]  M. Bridson,et al.  Metric Spaces of Non-Positive Curvature , 1999 .

[10]  S. Reich,et al.  Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings , 1984 .

[11]  Laurentiu Leustean,et al.  Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces , 2008, 0810.4117.

[12]  Wataru Takahashi,et al.  A convexity in metric space and nonexpansive mappings, I , 1970 .

[13]  Chi Song Wong,et al.  Quasi-nonexpansive multi-valued maps and selections , 1975 .

[14]  M. Abbas,et al.  Common fixed points of two multivalued nonexpansive maps in Kohlenbach hyperbolic spaces , 2014 .

[15]  W. R. Mann,et al.  Mean value methods in iteration , 1953 .

[16]  Hafiz Fukhar-ud-din,et al.  An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces , 2012 .