Approximate fixed point of uniform hemicontractive mapping and to apply to iterative solution of equation with uniform-accretive mapping

2013 ◽  
Vol 7 ◽  
pp. 1031-1040
Author(s):  
Xian Li ◽  
Huaxian Cai ◽  
Fang Xie ◽  
Yuguang Xu
Keyword(s):  
Fixed Point ◽  
Iterative Solution ◽  
Accretive Mapping ◽  
Approximate Fixed Point

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 On the approximate fixed point property in abstract spaces

2011 ◽  
Vol 271 (3-4) ◽  
pp. 1271-1285 ◽  
Author(s):  
C. S. Barroso ◽  
O. F. K. Kalenda ◽  
P.-K. Lin
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Point Property ◽  
Approximate Fixed Point ◽  
Approximate Fixed Point Property ◽  
Abstract Spaces

scholarly journals Convergence Rate of Some Two-Step Iterative Schemes in Banach Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
O. T. Wahab ◽  
R. O. Olawuyi ◽  
K. Rauf ◽  
I. F. Usamot
Keyword(s):  
Fixed Point ◽  
Convergence Rate ◽  
Banach Spaces ◽  
Numerical Approach ◽  
Normed Spaces ◽  
Mann Iteration ◽  
Ishikawa Iteration ◽  
Iterative Schemes ◽  
Approximate Fixed Point

This article proves some theorems to approximate fixed point of Zamfirescu operators on normed spaces for some two-step iterative schemes, namely, Picard-Mann iteration, Ishikawa iteration, S-iteration, and Thianwan iteration, with their errors. We compare the aforementioned iterations using numerical approach; the results show that S-iteration converges faster than other iterations followed by Picard-Mann iteration, while Ishikawa iteration is the least in terms of convergence rate. These results also suggest the best among two-step iterative fixed point schemes in the literature.

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