Generalized iteration methods for bounds of the solution of fixed point operator-equations

Computing ◽  
1980 ◽  
Vol 24 (2-3) ◽  
pp. 131-137 ◽  
Author(s):  
E. Kaucher ◽  
S. M. Rump
Keyword(s):  
Fixed Point ◽  
Operator Equations ◽  
Point Operator ◽  
Iteration Methods ◽  
Generalized Iteration

Optimal Feedback Design for Uncertain Systems: A Time-Domain Fixed-Point Approach in L∞

1993 ◽  
Vol 115 (3) ◽  
pp. 319-324
Author(s):  
R. Barnard ◽  
S. Beydoun
Keyword(s):  
Fixed Point ◽  
Time Domain ◽  
Uncertain Systems ◽  
Design Procedure ◽  
Tracking Errors ◽  
Operator Equations ◽  
Fixed Point Approach ◽  
Point Operator ◽  
Explicit Bounds ◽  
Dynamics Stability

This paper considers an alternative to quantitative feedback theory (QFT), an alternative deriving solely from a time-domain setting in Banach space L∞ and providing both a precise, amplitude-oriented design formulation and a general, computer-oriented design procedure. System dynamics, stability, and tracking are characterized as fixed-point operator equations and conditions under which tracking errors satisfy explicit bounds. The design formulation and procedure are illustrated by two design examples.

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 On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Jukkrit Daengsaen ◽  
Anchalee Khemphet
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Rate Of Convergence ◽  
Convergence Theorem ◽  
Computational Cost ◽  
Closed Intervals ◽  
Iteration Methods ◽  
Nondecreasing Functions ◽  
New Iterative Method

We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.

scholarly journals Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 218
Author(s):  
Lu-Chuan Ceng ◽  
Xiaoye Yang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mappings ◽  
General System ◽  
Inequality Constraint ◽  
Common Solution ◽  
Iteration Methods ◽  
Monotone Variational Inequality ◽  
Implicit Iteration

This paper discusses a monotone variational inequality problem with a variational inequality constraint over the common solution set of a general system of variational inequalities (GSVI) and a common fixed point (CFP) of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping in Hilbert spaces, which is called the triple hierarchical constrained variational inequality (THCVI), and introduces some Mann-type implicit iteration methods for solving it. Norm convergence of the proposed methods of the iteration methods is guaranteed under some suitable assumptions.

scholarly journals An Inflationary Fixed Point Operator in XQuery

2008 ◽  
Author(s):  
Loredana Afanasiev ◽  
Torsten Grust ◽  
Maarten Marx ◽  
Jan Rittinger ◽  
Jens Teubner
Keyword(s):  
Fixed Point ◽  
Point Operator

scholarly journals Fixed Point Theorems on Nonlinear Binary Operator Equations with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Baomin Qiao
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Operator ◽  
Order Theory ◽  
Iteration Theory ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Monotone Iteration ◽  
Binary Operator

The existence and uniqueness for solution of systems of some binary nonlinear operator equations are discussed by using cone and partial order theory and monotone iteration theory. Furthermore, error estimates for iterative sequences and some corresponding results are obtained. Finally, the applications of our results are given.

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