scholarly journals Hyers-Ulam stability of hyperbolic Möbius difference equation

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4555-4575 ◽  
Author(s):  
Young Nam
Keyword(s):  
Fixed Point ◽  
Difference Equation ◽  
Line Segment ◽  
Initial Point ◽  
Logistic Equation ◽  
Complex Numbers ◽  
Ulam Stability ◽  
The Difference ◽  
The Stability ◽  
Repelling Fixed Point

Hyers-Ulam stability of the difference equation with the initial point z0 as follows zi+1 = azi+b/czi+d is investigated for complex numbers a,b,c and d where ad-bc = 1, c ? 0 and a+d ?R\[-2,2]. The stability of the sequence {zn}n?N0 holds if the initial point is in the exterior of a certain disk of which center is ?d/c . Furthermore, the region for stability can be extended to the complement of some neighborhood of the line segment between -d/c and the repelling fixed point of the map z ? az+b/cz+d. This result is the generalization of Hyers-Ulam stability of Pielou logistic equation.

A FIXED POINT APPROACH TO THE STABILITY OF GENERAL QUADRATIC EULER-LAGRANGE FUNCTIONAL EQUATIONS IN INTUITIONISTIC FUZZY SPACES

2016 ◽  
pp. 4430-4436
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Fixed Point Approach ◽  
Intuitionistic Fuzzy ◽  
The Stability ◽  
Lagrange Functional ◽  
Intuitionistic Fuzzy Normed Spaces

In this paper, we prove the generalized Hyers-Ulam stability of a general k-quadratic Euler-Lagrange functional equation:for any fixed positive integer in intuitionistic fuzzy normed spaces using a fixed point method.

On the stability for the fuzzy initial value problem

2020 ◽  
Vol 39 (5) ◽  
pp. 7747-7755
Author(s):  
Ngo Van Hoa ◽  
Tofigh Allahviranloo ◽  
Ho Vu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Initial Value Problem ◽  
Ulam Stability ◽  
Initial Value ◽  
The Stability ◽  
Theoretical Results ◽  
Rassias Stability

In this paper, we present the Hyers–Ulam stability and Hyers–Ulam-Rassias stability (HU-stability and HUR-stability for short) for fuzzy initial value problem (FIVP) by using fixed point theorem. We improve and extend some known results on the stability for FDEs by dropping some assumptions. Some examples illustrate the theoretical results.

scholarly journals On the Recursive Sequencexn=A+xn−kp/xn−1r

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Fangkuan Sun ◽  
Xiaofan Yang ◽  
Chunming Zhang
Keyword(s):  
Difference Equation ◽  
Dynamic Behavior ◽  
Positive Solutions ◽  
Initial Conditions ◽  
Real Numbers ◽  
Positive Real ◽  
The Difference ◽  
The Stability

This paper studies the dynamic behavior of the positive solutions to the difference equationxn=A+xn−kp/xn−1r,n=1,2,…, whereA,p, andrare positive real numbers, and the initial conditions are arbitrary positive numbers. We establish some results regarding the stability and oscillation character of this equation forp∈(0,1).

scholarly journals Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

scholarly journals On the Stability of a Generalized Fréchet Functional Equation with Respect to Hyperplanes in the Parameter Space

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 384
Author(s):  
Janusz Brzdȩk ◽  
Zbigniew Leśniak ◽  
Renata Malejki
Keyword(s):  
Functional Equation ◽  
Exact Solution ◽  
Fixed Point ◽  
Approximate Solution ◽  
Fixed Point Theorem ◽  
Exact Solutions ◽  
Control Function ◽  
The Difference ◽  
The Stability ◽  
Ulam Type Stability

We study the Ulam-type stability of a generalization of the Fréchet functional equation. Our aim is to present a method that gives an estimate of the difference between approximate and exact solutions of this equation. The obtained estimate depends on the values of the coefficients of the equation and the form of the control function. In the proofs of the main results, we use a fixed point theorem to get an exact solution of the equation close to a given approximate solution.

scholarly journals On the Characterization of a Class of Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Muhammed Altun
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Toeplitz Matrices ◽  
Complex Banach Space ◽  
Asymptotic Behavior Of Solutions ◽  
Complex Numbers ◽  
Fixed Sequence ◽  
Lower Triangular ◽  
The Difference

We focus on the behavior of solutions of the difference equation , , where () is a fixed sequence of complex numbers, and () is a fixed sequence in a complex Banach space. We give the general solution of this difference equation. To examine the asymptotic behavior of solutions, we compute the spectra of operators which correspond to such type of difference equations. These operators are represented by upper triangular or lower triangular infinite banded Toeplitz matrices.

scholarly journals The Stability of a Quadratic Functional Equation with the Fixed Point Alternative

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Choonkil Park ◽  
Ji-Hye Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
The Stability

Lee, An and Park introduced the quadratic functional equationf(2x+y)+f(2x−y)=8f(x)+2f(y)and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.

scholarly journals New Method of Solving the Economic Complex Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Ya-Juan Yang ◽  
Chung-Cheng Chen ◽  
Yen-Ting Chen
Keyword(s):  
Difference Equation ◽  
Economic System ◽  
Optimization Problems ◽  
Direct Method ◽  
Economic Optimization ◽  
The Difference ◽  
Long Division ◽  
The Stability ◽  
Controllability And Observability ◽  
Z Transformation

In this study, the authors first develop a direct method used to solve the linear nonhomogeneous time-invariant difference equation with the same number for inputs and outputs. Economic cybernetics is the crystallization for the integration of economics and cybernetics. It analyzes the stability, controllability, and observability of the economic system by establishing a system model and enables people to better understand the characteristics of the economic system and solve economic optimization problems. The economic model generally applies the discrete recurrence difference equation. The significant analytic approach for the difference equation is the z-transformation technique. The z-transformation state of the economic cybernetics state-space difference equation generally is a rational function with the same power for the numerator and the denominator. The proposed approach will take the place of the traditional methods without all annoying procedures involving the long division of some complicated polynomials, the expanded multiplication of many polynomial factors, the differentiation of some complicated polynomials, and the complex derivations of all partial fraction parameters. To highlight the novelty of this research, this study especially applies the proposed theorems originally belonging to engineering to the field of economic applications.

A New Look at the Stability Analysis of Delay-Differential Equations

2005 ◽  
Author(s):  
Tama´s Kalma´r-Nagy
Keyword(s):  
Difference Equation ◽  
Differential Equations ◽  
Characteristic Equation ◽  
Delay Differential Equations ◽  
Linear Delay ◽  
The Laplace Transform ◽  
Method Of Steps ◽  
The Difference ◽  
The Stability ◽  
Delay Differential

It is shown that the method of steps for linear delay-differential equations combined with the Laplace-transform can be used to determine the stability of the equation. The result of the method is an infinite dimensional difference equation whose stability corresponds to that of the transcendental characteristic equation. Truncations of this difference equation are used to construct numerical stability charts. The method is demonstrated on a first and second order delay equation. Correspondence between the transcendental characteristic equation and the difference equation is proved for the first order case.

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