A new iterative scheme in CAT(0) spaces with convergence analysis

In this paper, we establish strong and ∆-convergence theorems in CAT(0) spaces for two total asymptotically nonexpansive non-self mappings via a new two-step iterative scheme for non-self-mappings. Our results extend and generalize several results from the current existing literature. c ©2017 All rights reserved.

[1]  M. Abbas,et al.  FIXED POINTS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE IN CAT(0) SPACES , 2013 .

[2]  Convergence of modified S-iteration process for two asymptotically nonexpansive mappings in the intermediate sense in CAT(0) spaces , 2014 .

[3]  S. Dashputre,et al.  Strong and ∆ − Convergence Theorems under a Recent Iterative Scheme in CAT ( 0 ) Spaces , 2016 .

[4]  W. A. Kirk,et al.  Topics in Metric Fixed Point Theory , 1990 .

[5]  William A. Kirk,et al.  A concept of convergence in geodesic spaces , 2008 .

[6]  M. Postolache,et al.  Three-step Iterations for Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces , 2017 .

[7]  Yeol Je Cho,et al.  Convergence theorems for mixed type asymptotically nonexpansive mappings , 2012 .

[8]  William A. Kirk,et al.  A FIXED POINT THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS , 1972 .

[9]  B. Panyanak.  On total asymptotically nonexpansive mappings in CAT(κ) spaces , 2014 .

[10]  William A. Kirk,et al.  Fixed points of uniformly lipschitzian mappings , 2006 .

[11]  M. S. Khan.  REMARKS ON SOME FIXED POINT THEOREMS , 1982 .

[12]  Commentationes Mathematicae Universitatis Carolinae.  Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces , 2012 .

[13]  A. Sahin,et al.  ON THE STRONG AND D-CONVERGENCE FOR TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPPINGS ON A CAT(0) SPACE , 2013 .

[14]  Shih-sen Chang,et al.  Convergence theorems for total asymptotically nonexpansive non-self mappings in CAT(0) spaces , 2013 .

[15]  Nawab Hussain,et al.  On asymptotic pointwise contractions in metric spaces , 2009 .

[16]  Li Yang,et al.  Demiclosed principle and Δ-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces , 2012, Appl. Math. Comput..

[17]  Habtu Zegeye,et al.  Approximating fixed points of total asymptotically nonexpansive mappings , 2006 .

[18]  Erdal Karapinar,et al.  Demiclosedness Principle for Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces , 2014, J. Appl. Math..

[19]  S. Dhompongsa,et al.  On -convergence theorems in CAT(0) spaces , 2008, Comput. Math. Appl..

[20]  Hong-Kun Xu,et al.  Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process , 1993 .

[21]  Bancha Panyanak,et al.  Demiclosed Principle for Asymptotically Nonexpansive Mappings in CAT(0) Spaces , 2010 .

[22]  H. Nashine,et al.  Strong and ∆-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces , 2017 .

[23]  J. Tang,et al.  Iterative Algorithm and $\mathrm{\Delta }$-Convergence Theorems for Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces , 2012 .

[24]  W. A. Kirk,et al.  An Introduction to Metric Spaces and Fixed Point Theory , 2001 .

[25]  Jacques Tits,et al.  Groupes Réductifs Sur Un Corps Local , 1972 .

[26]  An Implicit Algorithm for a Family of Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces , 2016 .

[27]  Mujahid Abbas,et al.  Strong and -convergence of some iterative schemes in CAT(0) spaces , 2011, Comput. Math. Appl..

[28]  Jürgen Schu,et al.  Iterative construction of fixed points of asymptotically nonexpansive mappings , 1991 .

[29]  Charles E. Chidume,et al.  Strong and weak convergence theorems for asymptotically nonexpansive mappings , 2003 .

[30]  Sebastian Ehrlichmann,et al.  Metric Spaces Of Non Positive Curvature , 2016 .

[31]  Fuhai Zhao,et al.  Strong and △-convergence theorems for total asymptotically nonexpansive nonself mappings in CAT(0) spaces , 2013 .

[32]  Strong and △-convergence theorems for two asymptotically nonexpansive mappings in the intermediate sense in CAT(0)$\operatorname{CAT}(0)$ spaces , 2015 .

[33]  S. Stević.  APPROXIMATING FIXED POINTS OF NONEXPANSIVE MAPPINGS , 2006 .