scholarly journals On Stability of Iterative Sequences with Error

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 765 ◽  
Author(s):  
Abed ◽  
Taresh
Keyword(s):  
Fixed Point ◽  
Unique Fixed Point ◽  
Contractive Mapping ◽  
Systems Of Equations ◽  
Operator Equations ◽  
Mann Iteration ◽  
Accretive Mappings ◽  
Non Linear Systems ◽  
Roots Of Equations ◽  
Linear Systems Of Equations

Iterative methods were employed to obtain solutions of linear and non-linear systems of equations, solutions of differential equations, and roots of equations. In this paper, it was proved that s-iteration with error and Picard–Mann iteration with error converge strongly to the unique fixed point of Lipschitzian strongly pseudo-contractive mapping. This convergence was almost F-stable and F-stable. Applications of these results have been given to the operator equations Fx=f and x+Fx=f, where F is a strongly accretive and accretive mappings of X into itself.

scholarly journals Iterative processes with errors for nonlinear equations

2004 ◽  
Vol 69 (2) ◽  
pp. 177-189 ◽  
Author(s):  
Łjubomir Ćirić ◽  
Jeong Sheok Ume
Keyword(s):  
Fixed Point ◽  
Nonlinear Equations ◽  
Unique Fixed Point ◽  
Convergence Theorems ◽  
Mann Iteration ◽  
General Lemma ◽  
Iterative Processes ◽  
Iteration Processes ◽  
Lipschitz Operators ◽  
Monotone Type

In this paper we introduce and consider a class of multi-valued and single-valued operators of generalised monotone type. We proved a new general lemma on the convergence of real sequences and some new convergence theorems for the Ishikawa and Mann iteration processes with errors to the unique fixed point of such operators, which are not necessarily Lipschitz operators. Our results generalise, improve, and extend several recent results.

scholarly journals Fixed point theorem with contractive mapping on C*-Algebra valued G-Metric Space

2021 ◽  
Vol 2106 (1) ◽  
pp. 012015
Author(s):  
A Wijaya ◽  
N Hariadi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Contractive Mapping ◽  
C Algebra ◽  
Metric Function ◽  
Interesting Theorem

Abstract Banach-Caccioppoli Fixed Point Theorem is an interesting theorem in metric space theory. This theorem states that if T : X → X is a contractive mapping on complete metric space, then T has a unique fixed point. In 2018, the notion of C *-algebra valued G-metric space was introduced by Congcong Shen, Lining Jiang, and Zhenhua Ma. The C *-algebra valued G-metric space is a generalization of the G-metric space and the C*-algebra valued metric space, meanwhile the G-metric space and the C *-algebra valued metric space itself is a generalization of known metric space. The G-metric generalized the domain of metric from X × X into X × X × X, the C *-algebra valued metric generalized the codomain from real number into C *-algebra, and the C *-algebra valued G-metric space generalized both the domain and the codomain. In C *-algebra valued G-metric space, there is one theorem that is similar to the Banach-Caccioppoli Fixed Point Theorem, called by fixed point theorem with contractive mapping on C *-algebra valued G-metric space. This theorem is already proven by Congcong Shen, Lining Jiang, Zhenhua Ma (2018). In this paper, we discuss another new proof of this theorem by using the metric function d(x, y) = max{G(x, x, y),G(y, x, x)}.

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