[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2020.28.4.915

COMMON FIXED POINT OF GENERALIZED ASYMPTOTIC POINTWISE (QUASI-) NONEXPANSIVE MAPPINGS IN HYPERBOLIC SPACES

Saleh, Khairul (Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals)
Fukhar-ud-din, Hafiz (Department of Mathematics The Islamia University of Bahawalpur)

Publication Information

Korean Journal of Mathematics / v.28, no.4, 2020 , pp. 915-929 More about this Journal

Abstract

We prove a fixed point theorem for generalized asymptotic pointwise nonexpansive mapping in the setting of a hyperbolic space. A one-step iterative scheme approximating common fixed point of two generalized asymptotic pointwise (quasi-) nonexpansive mappings in this setting is provided. We obtain ∆-convergence and strong convergence theorems of the iterative scheme for two generalized asymptotic pointwise nonexpansive mappings in the same setting. Our results generalize and extend some related results in the literature.

Keywords

Hyperbolic space; generalized asymptotic pointwise (quasi-) nonexpansive mapping; ${\Delta}$ -convergence; strong convergence; common fixed point; one-step iterative scheme;

Citations & Related Records

Reference

1	Chidume, C., Ofoedu, E.U., Zegeye, H., Strong and weak convergence theorems for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 280 (2003), 364-374. DOI
2	Fukhar-ud-din, H., Existence and approximation of fixed points in convex metric spaces, Carpathian J. Math. 30 (2014), 175-185. DOI
3	Fukhar-ud-din, H., Fixed point iterations in hyperbolic spaces, J Nonlinear Convex Anal., 2016. To appear.
4	Fukhar-ud-din, H., One step iteratiove scheme for a pair of nonexpansive mappings in a convex metric space, Hacet. J. Math. Stat. 44 (5) (2015), 1023-1031.
5	Fukhar-ud-din, H. Khamsi M.A. and Khan, A.R. Viscosity Iterative Method for a Finite Family of Generalized Asymptotically Quasi-nonexpansive Mappings in Convex Metric Spaces, J. Nonlinear Convex Anal., 16 (2015), 47-58.
6	Ishikawa, S., Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), 147-150. DOI
7	Khan, S. H., Convergence of a one-step iteration scheme for quasi-asymptotically nonexpansive mappings, World Academy of Science, Engineering and Technology 63 (2012), 504-506.
8	Kirk, W. and Panyanak, B., A concept of convergence in geodesic spaces, Nonlinear Anal. 68 (2008), 3689-3696. DOI
9	Khan, A.R., Khamsi, M.A. and Fukhar-ud-din, H., Strong convergence of a general iteration scheme in CAT(0)-spaces, Nonlinear Anal. 74 (2011), 783-791. DOI
10	Khan, S.H. and Takahashi, W., Approximating common fixed points of two asymptotically nonexpansive mappings, Sci. Math. Japon. 53 (2001), 133-138.
11	Kohlenbach, U., Some logical metatheorems with applications in functional analysis, Trans. Amer. Math. Soc. 357 (2005), 89-128. DOI
12	Mann, W.R., Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-610. DOI
13	Shimizu,T. and Takahashi, W. Fixed points of multivalued mappings in certain convex metric spaces, Topol. Methods Nonlinear Anal. 8 (1) (1996), 197-203. DOI
14	Tan, K.K. and Xu, H.K. Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), 301-308. DOI