scholarly journals Construction of Fixed Points of Asymptotically Nonexpansive Mappings in Uniformly Convex Hyperbolic Spaces

2021 ◽  
pp. 1-16
Author(s):  
Andrei Sipoş
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

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.

scholarly journals A Note on Common Fixed Point Results in Uniformly Convex Hyperbolic Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
W. Laowang ◽  
B. Panyanak
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Multivalued Mapping ◽  
Nonexpansive Mappings ◽  
Satisfying Condition ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

It is shown that the notion of mappings satisfying condition(K)introduced by Akkasriworn et al. (2012) is weaker than the notion of asymptotically quasi-nonexpansive mappings in the sense of Qihou (2001) and is weaker than the notion of pointwise asymptotically nonexpansive mappings in the sense of Kirk and Xu (2008). We also obtain a common fixed point for a commuting pair of a mapping satisfying condition(K)and a multivalued mapping satisfying condition(Cλ)for someλ∈(0,1). Our results properly contain the results of Abkar and Eslamian (2012), Akkasriworn et al. (2012), and many others.

scholarly journals Common Fixed Points Iteration Processes for a Finite Family of Asymptotically Nonexpansive Mappings

2004 ◽  
Vol 11 (1) ◽  
pp. 83-92
Author(s):  
Jui-Chi Huang
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Nonempty Closed Convex Subset ◽  
Convex Banach Space ◽  
Finite Family ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive ◽  
Iteration Processes ◽  
Suitable Sequence

Abstract Let 𝐸 be a uniformly convex Banach space which satisfies Opial's condition or its dual 𝐸* has the Kadec–Klee property, 𝐶 a nonempty closed convex subset of 𝐸, and 𝑇𝑗 : 𝐶 → 𝐶 an asymptotically nonexpansive mapping for each 𝑗 = 1, 2, . . . , 𝑟. Suppose {𝑥𝑛} is generated iteratively by where 𝑈𝑛(0) = 𝐼, 𝐼 is the identity map and {α 𝑛(𝑗)} is a suitable sequence in [0, 1]. If the set of common fixed points of is nonempty, then weak convergence of {𝑥𝑛} to some is obtained.

Sign in / Sign up

Export Citation Format

Share Document