Common fixed point of generalized asymptotic pointwise (quasi-) nonexpansive mappings in hyperbolic spaces
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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 $\triangle -$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.
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 $\triangle -$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.
참고문헌 (14)
- Chidume, C, "Strong and weak convergence theorems for asymptotically nonexpansive mappings", J. Math. Anal. Appl, 280, pp.364~374 (2003)
- Fukhar-ud-din, H., "Existence and approximation of fixed points in convex metric spaces", Carpathian J. Math, 30, pp.175~185 (2014)
- Fukhar-ud-din, H., "Fixed point iterations in hyperbolic spaces", J Nonlinear Convex Anal (2016)
- 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), pp.1023~1031 (2015)
- Fukhar-ud-din, H., "Viscosity Iterative Method for a Finite Family of Generalized Asymptotically Quasi-nonexpansive Mappings in Convex Metric Spaces", J. Nonlinear Convex Anal, 16, pp.47~58 (2015)
- Ishikawa, S., "Fixed points by a new iteration method", Proc. Amer. Math. Soc, 44, pp.147~150 (1974)
- Khan, S. H., "Convergence of a one-step iteration scheme for quasi-asymptotically nonexpansive mappings,World Academy of Science", Engineering and Technology, 63, pp.504~506 (2012)
- Kirk, W., "A concept of convergence in geodesic spaces", Nonlinear Anal, 68, pp.3689~3696 (2008)
- Khan, A.R., "Strong convergence of a general iteration scheme in CAT(0)-spaces", Nonlinear Anal, 74, pp.783~791 (2011)
- Khan, S.H., "Approximating common fixed points of two asymptotically nonexpansive mappings", Sci. Math. Japon, 53, pp.133~138 (2001)
- Kohlenbach, U., "Some logical metatheorems with applications in functional analysis", Trans. Amer. Math. Soc, 357, pp.89~128 (2005)
- Mann, W.R., "Mean value methods in iteration", Proc. Amer. Math. Soc, 4, pp.506~610 (1953)
- Shimizu,T., "Fixed points of multivalued mappings in certain convex metric spaces", Topol. Methods Nonlinear Anal., 8(1), pp.197~203 (1996)
- Tan, K.K., "Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process", J. Math. Anal. Appl., 178, pp.301~308 (1993)