TY - JOUR
T1 - Existence and approximation results for SKC mappings in CAT(0) spaces
AU - Abbas, Mujahid
AU - Khan, Safeer H
AU - Postolache, Mihai
PY - 2014/1/1
Y1 - 2014/1/1
N2 - Recently, Karapınar and Tas (Comput. Math. Appl. 61:3370-3380, 2011) extended the class of Suzuki-generalized nonexpansive mappings to the class of SKC mappings. In this paper, we investigate SKC mappings to get a criterion to guarantee a fixed point, via extending the results proved by Karapınar and Tas into the class of CAT(0) spaces. Further, by using Ishikawa-type iteration scheme for two mappings, we derive approximation fixed point sequence. Our results extend, improve and unify some existing results in this direction, such as (Nonlinear Anal. Hybrid Syst. 4:25-31, 2010) by Nanjaras et al. or (Comput. Math. Appl. 61:109-116, 2011) by Khan and Abbas. MSC:47H09, 47H10, 49M05.
AB - Recently, Karapınar and Tas (Comput. Math. Appl. 61:3370-3380, 2011) extended the class of Suzuki-generalized nonexpansive mappings to the class of SKC mappings. In this paper, we investigate SKC mappings to get a criterion to guarantee a fixed point, via extending the results proved by Karapınar and Tas into the class of CAT(0) spaces. Further, by using Ishikawa-type iteration scheme for two mappings, we derive approximation fixed point sequence. Our results extend, improve and unify some existing results in this direction, such as (Nonlinear Anal. Hybrid Syst. 4:25-31, 2010) by Nanjaras et al. or (Comput. Math. Appl. 61:109-116, 2011) by Khan and Abbas. MSC:47H09, 47H10, 49M05.
KW - common fixed point
KW - existence
KW - iterative process
KW - SKC mapping
KW - strong convergence
KW - Δ space
KW - △-convergence
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U2 - 10.1186/1029-242X-2014-212
DO - 10.1186/1029-242X-2014-212
M3 - Article
SN - 1025-5834
VL - 2014
JO - Journal of Inequalities and Applications
JF - Journal of Inequalities and Applications
IS - 1
M1 - 212
ER -