Some convergence results using a new implicit iteration process in CAT(0) space

Document Type : Research Paper

Authors

1 Department of Mathematics, Govt. College Israna, Panipat (Haryana)-132103, India

2 Department of Mathematics, S. K. Govt. College, Rewari (Haryana)-123401, India

3 Department of Mathematics, Maharshi Dayanand University, Rohtak (Haryana)-124001, India

10.22075/ijnaa.2024.27805.3717

Abstract

We prove the convergence of the newly defined iteration method to a common fixed point of a finite nonexpansive mappings family in CAT(0) space. A numerical example is given to check the convergence of the newly generalized iteration process. Many known results are extended and improved in this article.

Keywords

[1] M.R. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften, 319, Springer, Berlin, 1999.
[2] K.S. Brown, Buildings, Springer, New York, NY, USA, 1989.
[3] F. Bruhat and J. Tits, Reductive groups on a local field: I. Evaluated root data, Pub. Math. l’IHES 41 (1972), 5–251.
[4] D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry, Graduate Studies in Mathematics, American Mathematical Society Providence, 2001.
[5] C.E. Chidume and N. Shazad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62 (2005), 1149–1156.
[6] M. Gromov, Hyperbolic Groups, Essays in group theory, Math. Sci. Res. Inst. Publ., 8, Springer, New York, 1987.
[7] W.A. Kirk, Geodesic geometry and fixed point theory, Seminar Math. Anal. (Malaga/Seville,2002/2003), Colecc. Abierta. University Seville Secretary of Publications, Seville, Spain, 2003, pp. 195–225.
[8] W.A. Kirk, Geodesic geometry and fixed point theory II, Int. Conf. Fixed point Theory Appl., Yokohama Publishers, Yokohama, Japan, 2004, pp. 113–142.
[9] B. Xu and M.A. Noor, Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002), no. 2, 444–453.
[10] H.K. Xu and R. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001), 767–773.

Articles in Press, Corrected Proof
Available Online from 04 March 2024
  • Receive Date: 14 July 2022
  • Accept Date: 15 January 2024