TWO RESULTS ON APPROXIMATE FIXED POINTS OF NONEXPANSIVE MAPPINGS IN METRIC SPACES

2017 ◽  
Vol 11 (3) ◽  
pp. 185-196
Author(s):  
Simeon Reich ◽  
Alexander J. Zaslavski
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Nonexpansive Mappings

scholarly journals Approximations of Fixed Points in the Hadamard Metric Space CATp(0)

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1088
Author(s):  
Mostafa Bachar ◽  
Mohamed Amine Khamsi
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Metric Space ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Approximate Fixed Point ◽  
Successive Iteration ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

In this paper, we consider the recently introduced C A T p ( 0 ) , where the comparison triangles belong to ℓ p , for p ≥ 2 . We first establish an inequality in these nonlinear metric spaces. Then, we use it to prove the existence of fixed points of asymptotically nonexpansive mappings defined in C A T p ( 0 ) . Moreover, we discuss the behavior of the successive iteration introduced by Schu for these mappings in Banach spaces. In particular, we prove that the successive iteration generates an approximate fixed point sequence.

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