scholarly journals Existence and higher arity iteration for total asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Muhammad Aqeel Ahmad Khan ◽  
Hafiz Fukhar-ud-din ◽  
Amna Kalsoom
Keyword(s):  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

Three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in uniformly convex metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3573-3583
Author(s):  
Hafiz Fukhar-ud-dina ◽  
Safeer Khan
Keyword(s):  
Iterative Algorithm ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive Mappings ◽  
Convex Metric Spaces ◽  
Asymptotically Nonexpansive ◽  
Special Cases ◽  
Total Asymptotically Nonexpansive Mappings

We introduce and study a three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in a uniformly convex metric space. The proposed algorithm includes Mann and Ishikawa iterative algorithms, the iterative algorithm of Khan and Takahashi [13] and the three-step iterative algorithm of Xu and Noor [26] as special cases. Our results are new and generalize several recent results in Hilbert spaces, uniformly convex Banach spaces and CAT (0) spaces, simultaneously.

scholarly journals Common Fixed Points of Two Multivalued Asymptotically Nonexpansive Mappings

2019 ◽  
Vol 12 (2) ◽  
pp. 348-357
Author(s):  
Safeer Hussain Khan ◽  
Hira Iqbal ◽  
Mujahid Abbas
Keyword(s):  
Fixed Points ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Ishikawa Iterative Process

In this paper, we construct a modified Ishikawa iterative process to approximate common fixed points for two multivalued asymptotically nonexpansive mappings and prove some convergence theorems in uniformly convex hyperbolic spaces.

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