scholarly journals Hyers-Ulam Stability of Iterative Equation in the Class of Lipschitz Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Chao Xia ◽  
Wei Song
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Functional Equations ◽  
Convergent Sequence ◽  
Lipschitz Functions ◽  
Ulam Stability ◽  
Iterative Equation ◽  
Iterative Equations ◽  
Uniformly Convergent ◽  
Sequence Of Functions

Hyers-Ulam stability is a basic sense of stability for functional equations. In the present paper we discuss the Hyers-Ulam stability of a kind of iterative equations in the class of Lipschitz functions. By the construction of a uniformly convergent sequence of functions we prove that, for every approximate solution of such an equation, there exists an exact solution near it.

scholarly journals Ulam Stability for a Class of Hill’s Equations

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1483 ◽  
Author(s):  
Ryuma Fukutaka ◽  
Masakazu Onitsuka
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Stability Constants ◽  
Sufficient Condition ◽  
Ulam Stability ◽  
Necessary And Sufficient Condition ◽  
Hill’S Equation ◽  
Hill’S Equations ◽  
Necessary And Sufficient ◽  
Ulam’S Type Stability

This paper deals with Ulam’s type stability for a class of Hill’s equations. In the two assertions of the main theorem, we obtain Ulam stability constants that are symmetrical to each other. By combining the obtained results, a necessary and sufficient condition for Ulam stability of a Hill’s equation is established. The results are generalized to nonhomogeneous Hill’s equations, and then application examples are presented. In particular, it is shown that if the approximate solution is unbounded, then there is an unbounded exact solution.

scholarly journals Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Yongjin Li ◽  
Yan Shen
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Linear Differential ◽  
The Stability

The aim of this paper is to prove the stability in the sense of Hyers-Ulam of differential equation of second ordery′′+p(x)y′+q(x)y+r(x)=0. That is, iffis an approximate solution of the equationy′′+p(x)y′+q(x)y+r(x)=0, then there exists an exact solution of the equation near tof.

scholarly journals Hyers-Ulam stability of quadratic forms in 2-normed spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 496-502
Author(s):  
Won-Gil Park ◽  
Jae-Hyeong Bae
Keyword(s):  
Banach Spaces ◽  
Quadratic Forms ◽  
Functional Equations ◽  
Ulam Stability ◽  
Normed Spaces

AbstractIn this paper, we obtain Hyers-Ulam stability of the functional equationsf (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w),f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w)andf (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w)in 2-Banach spaces. The quadratic forms ax2 + bxy + cy2, ax2 + by2 and axy are solutions of the above functional equations, respectively.

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

scholarly journals The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 174-192
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Group ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

scholarly journals Functional equations in Schwartz distributions and their stabilities

2009 ◽  
Vol 3 (1) ◽  
pp. 14-26
Author(s):  
Jae-Young Chung
Keyword(s):  
Differential Equations ◽  
Functional Equations ◽  
Ulam Stability ◽  
Smooth Functions ◽  
Schwartz Distributions

Employing two methods we consider a class of n-dimensional functional equations in the space of Schwartz distributions. As the first approach, employing regularizing functions we reduce the equations in distributions to classical ones of smooth functions and find the solutions. Secondly, using differentiation in distributions, converting the functional equations to differential equations and find the solutions. Also we consider the Hyers-Ulam stability of the equations.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

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