Strong convergence theorems with a Noor-type iterative scheme in convex metric spaces

The paper introduces some new mappings in convex metric spaces, and then it considers a Noor-type iterative scheme to approximate common fixed points of an infinite family of uniformly quasi-sup(f"n)-Lipschitzian mappings and an infinite family of g"n-expansive mappings in convex metric spaces. Its results generalize, improve and unify some results in Chang et al. (2010) [13], Fukhar-ud-din and Khan (2007) [14], Liu et al. (2010) [17], Tian (2005) [7], Wang and Liu (2009) [19] and Wang et al. (2009) [20] under some appropriate conditions.

[1]  Muhammad Aslam Noor,et al.  Some developments in general variational inequalities , 2004, Appl. Math. Comput..

[2]  Chao Wang,et al.  Approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces , 2009, Appl. Math. Comput..

[3]  M. Noor.  New approximation schemes for general variational inequalities , 2000 .

[4]  Muhammad Aslam Noor,et al.  Three-step methods for nonexpansive mappings and variational inequalities , 2007, Appl. Math. Comput..

[5]  Muhammad Aslam Noor,et al.  Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces , 2002 .

[6]  You-Xian Tian.  Convergence of an Ishikawa type iterative scheme for asymptotically quasi-nonexpansive mappings , 2005 .

[7]  Suthep Suantai,et al.  Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings , 2005 .

[8]  Li Yang,et al.  Stronger convergence theorems for an infinite family of uniformly quasi-Lipschitzian mappings in convex metric spaces , 2010, Appl. Math. Comput..

[9]  Suthep Suantai,et al.  The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces , 2007, Appl. Math. Comput..

[10]  Chao Wang,et al.  Convergence theorems for fixed points of uniformly quasi-Lipschitzian mappings in convex metric spaces , 2009 .

[11]  Muhammad Aslam Noor,et al.  Convergence of three-step iterations for asymptotically nonexpansive mappings , 2007, Appl. Math. Comput..

[12]  Muhammad Aslam Noor,et al.  Extended general variational inequalities , 2009, Appl. Math. Lett..

[13]  M. Noor,et al.  Some aspects of variational inequalities , 1993 .

[14]  Safeer Hussain Khan,et al.  Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications , 2007 .

[15]  Abdul Rahim Khan,et al.  Convergence of a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications , 2010, Comput. Math. Appl..

[16]  Tian You-xian,et al.  Convergence Theorems of Three-Step Iterative Scheme for a Finite Family of Uniformly Quasi-Lipschitzian Mappings in Convex Metric Spaces , 2009 .

[17]  Hafiz Fukhar-ud-din,et al.  Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces , 2008 .

[18]  Nan-Jing Huang,et al.  Approximating the common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex metric spaces , 2010, Appl. Math. Comput..