scholarly journals Fixed Point and Newton’s Methods in the Complex Plane

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
François Dubeau ◽  
Calvin Gnang
Keyword(s):  
Fixed Point ◽  
Complex Plane ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Newton's Methods

We revisit the necessary and sufficient conditions for linear and high order of convergence of fixed point and Newton’s methods in the complex plane. Schröder’s processes of the first and second kind are revisited and extended. Examples and numerical experiments are included.

The M/M/1 queue with mass exodus and mass arrivals when empty

1997 ◽  
Vol 34 (01) ◽  
pp. 192-207 ◽  
Author(s):  
Anyue Chen ◽  
Eric Renshaw
Keyword(s):  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Positive Recurrence ◽  
Powerful Technique ◽  
Resolvent Approach ◽  
Necessary And Sufficient ◽  
Direct Attack

An M/M/1 queue is subject to mass exodus at rate β and mass immigration at rate when idle. A general resolvent approach is used to derive occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.

scholarly journals Admissibility of Fractional Order Descriptor Systems Based on Complex Variables: An LMI Approach

2020 ◽  
Vol 4 (1) ◽  
pp. 8
Author(s):  
Xuefeng Zhang ◽  
Yuqing Yan
Keyword(s):  
Fractional Order ◽  
Complex Plane ◽  
Sufficient Conditions ◽  
Complex Variables ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
Fractional Order Systems ◽  
Lmi Approach ◽  
Numerical Examples ◽  
Necessary And Sufficient

This paper is devoted to the admissibility issue of singular fractional order systems with order α ∈ ( 0 , 1 ) based on complex variables. Firstly, with regard to admissibility, necessary and sufficient conditions are obtained by strict LMI in complex plane. Then, an observer-based controller is designed to ensure system admissible. Finally, numerical examples are given to reveal the validity of the theoretical conclusions.

scholarly journals Magnifying Elements in Semigroups of Fixed Point Set Transformations Restricted by an Equivalence Relation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Thananya Kaewnoi ◽  
Ronnason Chinram ◽  
Montakarn Petapirak
Keyword(s):  
Fixed Point ◽  
Equivalence Relation ◽  
Nonempty Subset ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Fixed Point Set ◽  
Point Set ◽  
Necessary And Sufficient ◽  
Semigroup Of Transformations

Let X be a nonempty set and ρ be an equivalence relation on X . For a nonempty subset S of X , we denote the semigroup of transformations restricted by an equivalence relation ρ fixing S pointwise by E F S X , ρ . In this paper, magnifying elements in E F S X , ρ will be investigated. Moreover, we will give the necessary and sufficient conditions for elements in E F S X , ρ to be right or left magnifying elements.

scholarly journals Fixed point theory in the setting of $(\alpha,\beta,\psi,\phi)$-interpolative contractions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Erdal Karapınar ◽  
Andreea Fulga ◽  
Antonio Francisco Roldán López de Hierro
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Necessary And Sufficient Conditions ◽  
Alpha Beta ◽  
Necessary And Sufficient

AbstractIn this manuscript we introduce the notion of $(\alpha,\beta,\psi,\phi)$ ( α , β , ψ , ϕ ) -interpolative contraction that unifies and generalizes significant concepts: Proinov type contractions, interpolative contractions, and ample spectrum contraction. We investigate the necessary and sufficient conditions to guarantee existence and uniqueness of the fixed point of such mappings.

scholarly journals Fixed point theorems for non-self maps I

1994 ◽  
Vol 17 (4) ◽  
pp. 713-716 ◽  
Author(s):  
Troy L. Hicks ◽  
Linda Marie Saliga
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Closed Subset ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Sufficient Conditions ◽  
General Setting ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

Supposef:C→XwhereCis a closed subset ofX. Necessary and sufficient conditions are given forfto have a fixed point. All results hold whenXis complete metric space. Several results hold in a much more general setting.

scholarly journals High-Order Iterative Methods for the DMP Inverse

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Xiaoji Liu ◽  
Naping Cai
Keyword(s):  
Error Estimate ◽  
Iterative Methods ◽  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Sufficient Conditions For Convergence ◽  
Necessary And Sufficient ◽  
High Order Iterative Methods

We investigate two iterative methods for computing the DMP inverse. The necessary and sufficient conditions for convergence of our schemes are considered and the error estimate is also derived. Numerical examples are given to test the accuracy and effectiveness of our methods.

Asymptotic Behaviour of Nonoscillatory Equations

1983 ◽  
Vol 35 (3) ◽  
pp. 436-453 ◽  
Author(s):  
Allan L. Edelson ◽  
Emilia Perri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Operator ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Bounded Solutions ◽  
Nonoscillatory Solutions ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Asymptotic Forms

For nonlinear equations of the formIthere has been considerable interest in determining the asymptotic forms of nonoscillatory solutions. We assume r(t) is continuous and positive on [0, ∞), and f(t, x) is continuous on [0, ∞) × R, and f(t, x) ≥ 0 for x ≠ 0. For n = 2, equation (I) was studied by Kusano and Naito [3], who found necessary and sufficient conditions for the existence of minimal and maximal nonoscillatory solutions. The former are the bounded solutions, while the later are those asymptotic to the function1.1Their method consisted of writing (I) in the form of an integral operator and applying the Schauder fixed point theorem. For arbitrary n, but for r(t) = 1, Kreith [2] found necessary and sufficient conditions for the existence of maximal solutions.

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