Existence and approximation results for SKC mappings in CAT(0) spaces

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Authors

Abbas, Mujahid
Khan, Safeer Hussain
Postolache, Mihai

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SpringerOpen

Abstract

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.

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Keywords

Iterative process, SKC mapping, Existence, Common fixed point, Strong convergence, CAT(0) space, △-convergence

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Citation

Abbas, M, Khan, SH & Postolache, M 2014, 'Existence and approximation results for SKC mappings in CAT(0) spaces', Journal of Inequalities and Applications, vol. 2014, art. no. 212, pp. 1-10.