scholarly journals Fixed-point iteration processes for non-Lipschitzian mappings of asymptotically quasi-nonexpansive type

2003 ◽  
Vol 2003 (33) ◽  
pp. 2075-2081 ◽  
Author(s):  
Daya Ram Sahu ◽  
Jong Soo Jung
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Iteration ◽  
Ishikawa Iteration ◽  
Lipschitzian Mappings ◽  
Iteration Processes

We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach 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.

scholarly journals Approximating the zeros of accretive operators by the Ishikawa iteration process

1996 ◽  
Vol 1 (2) ◽  
pp. 153-167 ◽  
Author(s):  
Zhou Haiyun ◽  
Jia Yuting
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Iteration Process ◽  
Accretive Operators ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
Uniformly Smooth ◽  
Ishikawa Iteration Process ◽  
Uniformly Smooth Banach Spaces ◽  
Iteration Processes

Some strong convergence theorems are established for the Ishikawa iteration processes for accretive operators in uniformly smooth Banach spaces.

APPROXIMATING THE SOLUTION OF A FRACTIONAL ORDER MODEL OF NOVEL CORONAVIRUS (COVID-2019) UNDER CAPUTO–FABRIZIO DERIVATIVE

2021 ◽  
Vol 11 (1) ◽  
pp. 35-46
Author(s):  
F.A. Adie ◽  
G.I. Ogban ◽  
S.E. Ekoro ◽  
O. Joseph ◽  
A.E. Ofem
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fractional Order ◽  
Iteration Method ◽  
Order Model ◽  
Fixed Point Iteration ◽  
Fractional Order Model ◽  
Novel Coronavirus

This paper presents a fixed point iteration method for approximating the solution of a fractional order model of novel coronavirus (COVID-2019) under Caputo--Fabrizio derivative in Banach spaces. Our result is new and complements some existing results in the literature.

scholarly journals Implicit Ishikawa Approximation Methods for Nonexpansive Semigroups in CAT(0) Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhi-bin Liu ◽  
Yi-shen Chen ◽  
Xue-song Li ◽  
Yi-bin Xiao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Nonexpansive Semigroup ◽  
Approximation Methods ◽  
Ishikawa Iteration ◽  
Nonexpansive Semigroups ◽  
Convergence Results ◽  
Iteration Processes

This paper is devoted to the convergence of the implicit Ishikawa iteration processes for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain theΔ-convergence results of the implicit Ishikawa iteration sequences for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Ishikawa iteration sequences for nonexpansive semigroups in the CAT(0) spaces. The results presented in this paper extend and generalize some previous results.

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