scholarly journals Approximation of random fixed points of non-self asymptotically nonexpansive random mappings

2007 ◽  
Vol 2 ◽  
pp. 1859-1868 ◽  
Author(s):  
Xin-Wei Zhou ◽  
Lin Wang
Keyword(s):  
Fixed Points ◽  
Random Fixed Points ◽  
Asymptotically Nonexpansive ◽  
Random Mappings

scholarly journals On Common Random Fixed Points of a New Iteration with Errors for Nonself Asymptotically Quasi-Nonexpansive Type Random Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
R. A. Rashwan ◽  
P. K. Jhade ◽  
Dhekra Mohammed Al-Baqeri
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Separable Banach Space ◽  
Iterative Scheme ◽  
Random Fixed Points ◽  
Real Separable Banach Space ◽  
Random Mappings

We prove some strong convergence of a new random iterative scheme with errors to common random fixed points for three and then N nonself asymptotically quasi-nonexpansive-type random mappings in a real separable Banach space. Our results extend and improve the recent results in Kiziltunc, 2011, Thianwan, 2008, Deng et al., 2012, and Zhou and Wang, 2007 as well as many others.

Random fixed points of asymptotically nonexpansive random operators on unbounded domains

2008 ◽  
Vol 58 (6) ◽  
Author(s):  
Ismat Beg ◽  
Mujahid Abbas
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Unbounded Domains ◽  
Random Operator ◽  
Random Operators ◽  
Random Fixed Point ◽  
Random Fixed Points ◽  
Asymptotically Nonexpansive

AbstractThe aim of this paper is to prove some random fixed point theorems for asymptotically nonexpansive random operator defined on an unbounded closed and starshaped subset of a Banach space.

RANDOM COINCIDENCE AND FIXED POINTS FOR WEAKLY COMPATIBLE MAPPINGS IN CONVEX METRIC SPACES

2009 ◽  
Vol 02 (02) ◽  
pp. 171-182 ◽  
Author(s):  
Izmat Beg ◽  
Adnan Jahangir ◽  
Akbar Azam
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Coincidence Points ◽  
Random Coincidence ◽  
Complete Metric Spaces ◽  
Random Fixed Points ◽  
Weakly Compatible ◽  
Convex Metric Spaces

Some new theorems on random coincidence points and random fixed points for weakly compatible mappings in convex separable complete metric spaces have been established. These results generalize some recent well known comparable results in the literature.

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.

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