Approximating common fixed points of total asymptotically nonexpansive mappings in CAT(0) spaces
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Authors
Hafiz Fukhar-ud-din
- Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
Abdul Rahim Khan
- Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
Nawab Hussain
- Department of Mathematics, King Abdul Aziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Abstract
We introduce and study convergence of a one-step iterative algorithm for a finite family of total asymptotically nonexpansive
mappings on a CAT(0) space. Our results are new in Hilbert spaces as well as CAT(0) spaces; in particular, an analogue of
Rhoades weak convergence theorem [B. E. Rhoades, Bull. Austral. Math. Soc., 62 (2000), 307–310] is established both for
\(\Delta\)-convergence and strong convergence in CAT(0) spaces.
Share and Cite
ISRP Style
Hafiz Fukhar-ud-din, Abdul Rahim Khan, Nawab Hussain, Approximating common fixed points of total asymptotically nonexpansive mappings in CAT(0) spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 771--779
AMA Style
Fukhar-ud-din Hafiz, Khan Abdul Rahim, Hussain Nawab, Approximating common fixed points of total asymptotically nonexpansive mappings in CAT(0) spaces. J. Nonlinear Sci. Appl. (2017); 10(2):771--779
Chicago/Turabian Style
Fukhar-ud-din, Hafiz, Khan, Abdul Rahim, Hussain, Nawab. "Approximating common fixed points of total asymptotically nonexpansive mappings in CAT(0) spaces." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 771--779
Keywords
- CAT(0) space
- total asymptotically nonexpansive mapping
- one-step iterative algorithm
- common fixed point
- \(\Delta\)-convergence
- strong convergence.
MSC
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