scholarly journals On Faster Implicit Hybrid Kirk-Multistep Schemes for Contractive-Type Operators

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
O. T. Wahab ◽  
K. Rauf
Keyword(s):  
Convergence Rate ◽  
Strong Convergence ◽  
Numerical Approach ◽  
Type Operator ◽  
Linear Spaces ◽  
Hybrid Schemes ◽  
Iterative Schemes ◽  
Normed Linear Spaces ◽  
Contractive Type ◽  
Stability Results

The purpose of this paper is to prove strong convergence and T-stability results of some modified hybrid Kirk-Multistep iterations for contractive-type operator in normed linear spaces. Our results show through analytical and numerical approach that the modified hybrid schemes are better in terms of convergence rate than other hybrid Kirk-Multistep iterative schemes in the literature.

Common fixed point of Jungck-Kirk-type iterations for non-self operators in normed linear spaces

2016 ◽  
Vol 56 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Hudson Akewe ◽  
Adesanmi Mogbademu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Linear Space ◽  
Normed Linear Space ◽  
Linear Spaces ◽  
Iterative Schemes ◽  
Normed Linear Spaces ◽  
The Common ◽  
Stability Results

Abstract In this paper, we introduce Jungck-Kirk-multistep and Jungck-Kirk-multistep-SP iterative schemes and use their strong convergences to approximate the common fixed point of nonself operators in a normed linear Space. The Jungck-Kirk-Noor, Jungck-Kirk-SP, Jungck-Kirk-Ishikawa, Jungck-Kirk-Mann and Jungck-Kirk iterative schemes follow our results as corollaries. We also study and prove stability results of these schemes in a normed linear space. Our results generalize and unify most approximation and stability results in the literature.

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 Convergence and Stability of New Approximation Algorithms for Certain Contractive-Type Mappings

2021 ◽  
Vol 2 ◽  
pp. 1
Author(s):  
Imo Kalu Agwu ◽  
Donatus Ikechi Igbokwe
Keyword(s):  
Approximation Algorithms ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Type Condition ◽  
Iterative Schemes ◽  
Convergence And Stability ◽  
Contractive Type ◽  
Stability Results

We present new fixed points algorithms called multistep H-iterative scheme and multistep SH-iterative scheme. Under certain contractive-type condition, convergence and stability results were established without any imposition of the ’sum conditions’, which to a large extent make some existing iterative schemes so far studied by other authors in this direction practically inefficient. Our results complement and improve some recent results in literature.

scholarly journals Viscosity Approximation Methods for a Family of Nonexpansive Mappings in CAT(0) Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Jinfang Tang
Keyword(s):  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Approximation Methods ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Convergence Problem ◽  
Iterative Schemes ◽  
The Family ◽  
Viscosity Approximation Methods ◽  
Implicit And Explicit

The purpose of this paper is using the viscosity approximation method to study the strong convergence problem for a family of nonexpansive mappings in CAT(0) spaces. Under suitable conditions, some strong convergence theorems for the proposed implicit and explicit iterative schemes to converge to a common fixed point of the family of nonexpansive mappings are proved which is also a unique solution of some kind of variational inequalities. The results presented in this paper extend and improve the corresponding results of some others.

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