Fixed point iterations of asymptotically demicontractive and asymptotically hemicontractive mappings in hyperbolic spaces

References

• 1. B. Beauzamy, Introduction to Banach Spaces and their Geometry (North-Holland, Amsterdam, 1985). Google Scholar
• 2. C. E. Chidume and C. Moore, Fixed points iteration for pseudocontractive maps, Proc. Amer. Math. Soc. 127(4) (1999) 1163–1170. Crossref, Web of Science, Google Scholar
• 3. Y. J. Cho, H. Zhou and S. M. Kang, Strong convergence theorems for iterative schemes with errors for asymptotically demicontractive mappings in arbitrary real normed linear spaces, J. Inequal. Pure Appl. Math. 3 (2002) 1–11. Google Scholar
• 4. B. A. Ibn Dehaish, M. A. Khamsi and A. R. Khan, Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces, J. Math. Anal. Appl. 397 (2013) 861–868. Crossref, Web of Science, Google Scholar
• 5. S. Ishikawa, Fixed point by a new iteration method, Proc. Amer. Math. Soc. 44 (1974) 147–150. Crossref, Web of Science, Google Scholar
• 6. M. A. Khamsi and A. R. Khan, Inequalities in metric spaces with applications, Nonlinear Anal. 74 (2011) 4036–4045. Crossref, Web of Science, Google Scholar
• 7. W. A. Kirk, A fixed point theorem in CAT$(0)$ spaces and $ℝ$-trees, Fixed Point Theory Appl. 4 (2004) 309–316. Google Scholar
• 8. W. A. Kirk, Fixed Point Theory for Nonexpansive Mappings, I and II, Lecture Notes in Mathematics, Vol. 886 (Springer, Berlin, 1981), pp. 485–505. Google Scholar
• 9. L. Leustean, A quadratic rate of asymptotic regularity for CAT$(0)$-spaces, J. Math. Anal. Appl. 325 (2007) 386–399. Crossref, Web of Science, Google Scholar
• 10. W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953) 506–510. Crossref, Web of Science, Google Scholar
• 11. K. Menger, Untersuchungen über allgemeine Metrik, Math. Ann. 100 (1928) 75–163. Crossref, Google Scholar
• 12. J. O. Olaleru and G. A. Okeke, Convergence theorems on asymptotically demicontractive and hemicontractive mappings in the intermediate sense, Fixed Point Theory Appl. 2013 (2013) 352. Crossref, Google Scholar
• 13. L. Qihou, On Naimpally and Singh’s open questions, J. Math. Anal. Appl. 124 (1987) 157–164. Crossref, Web of Science, Google Scholar
• 14. L. Qihou, The convergence theorems of the sequence of Ishikawa iterates for hemicontractive mappings, J. Math. Anal. Appl. 148 (1990) 55–62. Crossref, Web of Science, Google Scholar
• 15. L. Qihou, Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings, Nonlinear Anal. 26(11) (1996) 1835–1842. Crossref, Web of Science, Google Scholar
• 16. J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991) 407–413. Crossref, Web of Science, Google Scholar
• 17. W. Takahashi, A convexity in metric spaces and nonexpansive mappings, Kodai Math. Sem. Rep. 22 (1970) 142–149. Crossref, Google Scholar
• 18. K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993) 301–308. Crossref, Web of Science, Google Scholar
• 19. H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. 16 (1991) 1127–1138. Crossref, Web of Science, Google Scholar