Fixed point theorem for asymptotically nonexpansive mappings under a new iteration sequence in CAT(0) space

Document Type : Research Paper


1 Mathematics Science, Ministry of Education, Directorate of Education Baghdad Al-Rusafa 1{st}, Iraq

2 Department of mathematics, College of Education for pure science (Ibn-ALHaitham), university of Baghdad, Baghdad, Iraq


This paper is to define a new iterative scheme under a special sequence of asymptotically nonexpansive mapping with a special sequence. We prove some convergence, existence in {CAT(0)} space.


[1] M.R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, vol. 319. Springer Science & Business Media, 2013.
[2] F. Bruhat and J. Tits, Groupes r´eductifs sur un corps local, Publ. Math.Institut Hautes Etudes Sci. 41 (1972) ´ 5–251.
[3] S. Dhompongsa, W. A. Kirk and B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal. 8 (2007).
[4] S. Dhompongsa, W.A. Kirk and B. Sims, Fixed points of uniformly Lipschitzian mappings, Nonlinear Anal. Theory, Methods Appl. 65 (2006) 762–772.
[5] S. Dhompongsa and B. Panyanak, On ∆ϵ convergence theorems in CAT (0) spaces, Comput. Math. Appl. 56 (2008) 2572–2579.
[6] W.A. Kirk, Geodesic geometry and fixed point theory, In Seminar of mathematical analysis (Malaga/Seville), 2002/2003), 64 (2003) 195–225.
[7] W.A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. Theory, Methods Appl. 68 (2008) 3689–3696.
[8] T.C. Lim, Remarks on some fixed point theorems, Proc. Am. Math. Soc. 60 (1976) 179–182.
[9] S.H. Malih, Common Fixed Point for a Pair of Asymptotically Nonexpansive and Multivalued Mapping Under Fibonacci Iteration Sequence in CAT (0) Space, J. Phys. Conf. Ser. 1879 (2021).
[10] S.H. Malih and S.S. Abed, Approximating random fixed points under a new iterative sequence, J. Interdiscip. Math. 22 (2019) 1407–1414.
[11] S.H. Malih, Fixed point theorems of modified Mann and Ishikawa iterations, J. Interdiscip. Math. 24 (2021) 1093–1097.
[12] S.H. Malih, Stability and convergence theorems of pointwise asymptotically nonexpansive random operator in Banach space, Int. J. Nonlinear Anal. Appl. 12 (2021) 119–127.
[13] S.H. Malih, Random fixed point for random Fibonacci Noor iteration scheme, J. Interdiscip. Math., 24 (2021) 775–779.
[14] S.H. Malih, Random fixed point under contractive condition of integral type, J. Phys. Conf. Ser. 1897 (2021) 12035.
[15] S.H. Malih, Random Fixed Point on Ishikawa Random Iteration Under Fibonacci Sequence, J. Phys. Conf. Ser. 1879 (2021) 32044.
[16] S.H. Malih and S.S. Abed, Convergence and stability of some random iterative schemes, J. Phys.: Conf. Ser. 1963 (2021) 12112.
[17] S.H. Malih and S.S. Abed, Convergence of random iterative scheme to a common random fixed points, J. Phys. Conf. Ser. 1963 (2021) 12113.
[18] B. Nanjaras and B. Panyanak, Demiclosed principle for asymptotically nonexpansive mappings in CAT (0) spaces, Fixed Point Theory Appl. 2010 (2010) 268780.
[19] Y. Niwongsa and B. Panyanak, Noor iterations for asymptotically nonexpansive mappings in CAT (0) spaces, Int. J. Math. Anal. 4 (2010) 645–656.
[20] H. Zhou, R.P. Agarwal, Y.J. Cho and Y.S. Kim, Nonexpansive mappings and iterative methods in uniformly convex Banach spaces, Georg. Math. J. 9 (2002) 591–600.
Volume 13, Issue 1
March 2022
Pages 685-691
  • Receive Date: 02 August 2021
  • Revise Date: 15 September 2021
  • Accept Date: 21 September 2021