scholarly journals Approximating Common Fixed Points of an Evolution Family on a Metric Space via Mann Iteration

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Liang Luo ◽  
Rizwan Ullah ◽  
Gul Rahmat ◽  
Saad Ihsan Butt ◽  
Muhammad Numan
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Irrational Number ◽  
Iteration Process ◽  
Common Fixed Points ◽  
Evolution Family ◽  
Mann Iteration ◽  
The Family ◽  
Families Of Operators ◽  
Mann Iteration Process

In this article, we present the set of all common fixed points of a subfamily of an evolution family in terms of intersection of all common fixed points of only two operators from the family; that is, for subset M of L , we have F M = F Y ϱ 1 , 0 ∩ F Y ϱ 2 , 0 , where ϱ 1 and ϱ 2 are positive and ϱ 1 / ϱ 2 is an irrational number. Furthermore, we approximate such common fixed points by using the modified Mann iteration process. In fact, we are generalizing the results from a semigroup of operators to evolution families of operators on a metric space.

scholarly journals An iteration process for common fixed points of two nonself asymptotically nonexpansive mappings

2012 ◽  
Vol 20 (1) ◽  
pp. 15-30 ◽  
Author(s):  
Sezgin Akbulut
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Contemporary Literature ◽  
Iteration Process ◽  
Common Fixed Points ◽  
Weak And Strong Convergence ◽  
Mann Iteration ◽  
Asymptotically Nonexpansive ◽  
Ishikawa Iteration Process ◽  
Mann Iteration Process

Abstract In this paper, we introduce an iteration process for approximating common fixed points of two nonself asymptotically nonexpansive map- pings in Banach spaces. Our process contains Mann iteration process and some other processes for nonself mappings but is independent of Ishikawa iteration process. We prove some weak and strong convergence theorems for this iteration process. Our results generalize and improve some results in contemporary literature.

scholarly journals Approximate Fixed Point Sequences of an Evolution Family on a Metric Space

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Si Fuan ◽  
Rizwan Ullah ◽  
Gul Rahmat ◽  
Muhammad Numan ◽  
Saad Ihsan Butt ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Nonlinear Operator ◽  
Iteration Process ◽  
Evolution Family ◽  
Nonlinear Mapping ◽  
Approximate Fixed Point ◽  
The Family ◽  
Ishikawa Iteration Process ◽  
The Common

In this article, we study the approximate fixed point sequence of an evolution family. A family E=Ux,y;x≥y≥0 of a bounded nonlinear operator acting on a metric space M,d is said to be an evolution family if Ux,x=I and Ux,yUy,z=Ux,z for all x≥y≥z≥0. We prove that the common approximate fixed point sequence is equal to the intersection of the approximate fixed point sequence of two operators from the family. Furthermore, we apply the Ishikawa iteration process to construct an approximate fixed point sequence of an evolution family of nonlinear mapping.

scholarly journals The Convergence of Mann Iteration for Generalized Φ- hemi-contractive Maps

2020 ◽  
pp. 39-52
Author(s):  
Linxin Li ◽  
Dingping Wu
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Iteration Process ◽  
Smooth Banach Space ◽  
Mann Iteration ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth ◽  
Contractive Maps ◽  
Mann Iteration Process

Abstract Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ − accretive and fixed points of strongly Φ− hemi-contractive we extend the results to Mann-type iterative and Mann iteration process with errors.

scholarly journals Existence of common fixed points via modified mann iteration in convex metric spaces and an invariant approximation result

2010 ◽  
Vol 41 (4) ◽  
pp. 335-348
Author(s):  
G.V.R. Babu ◽  
G.N. Alemayehu
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Convex Metric Space ◽  
Approximation Result ◽  
Mann Iteration ◽  
Invariant Approximation ◽  
Convex Metric Spaces ◽  
Weakly Contractive

We prove the existence of common fixed points for two selfmaps $T$ and $f$ of a convex metric space $X$ via the convergence of modified Mann iteration where $T$ is a nonlinear $f$-weakly contractive selfmap of $X$ and range of $f$ is complete. An invariant approximation result is also proved.

Common fixed points for multimaps in a metric space

1989 ◽  
Vol 13 (3) ◽  
pp. 221-229 ◽  
Author(s):  
K.P.R. Sastry ◽  
S.V.R. Naidu ◽  
J.R. Prasad
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Common Fixed Points

scholarly journals Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 481 ◽  
Author(s):  
Buthinah Dehaish ◽  
Mohamed Khamsi
Keyword(s):  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Modular Function ◽  
Function Spaces ◽  
Mann Iteration ◽  
Modular Spaces ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Modular Function Spaces ◽  
Mann Iteration Process

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci–Mann iteration process, introduced recently by Alfuraidan and Khamsi, defined by

Common fixed points for maps on metric space with w-distance

2008 ◽  
Vol 199 (2) ◽  
pp. 599-610 ◽  
Author(s):  
Dejan Ilić ◽  
Vladimir Rakočević
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Common Fixed Points
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