Results 11 to 20 of about 2,495 (216)

On a Generalized Hyers‐Ulam Stability of Trigonometric Functional Equations [PDF]

Journal of Applied Mathematics, 2012
Let G be an Abelian group, let ℂ be the field of complex numbers, and let f, g : G → ℂ. We consider the generalized Hyers‐Ulam stability for a class of trigonometric functional inequalities, |f(x − y) − f(x)g(y) + g(x)f(y)| ≤ ψ(y),  |g(x − y) − g(x)g(y) − f(x)f(y)| ≤ ψ(y), where ψ : G → ℝ is an arbitrary nonnegative function.
Chung, Jaeyoung, Chang, Jeongwook
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On Generalized Hyers‐Ulam Stability of Admissible Functions [PDF]

Abstract and Applied Analysis, 2012
We consider the Hyers‐Ulam stability for the following fractional differential equations in sense of Srivastava‐Owa fractional operators (derivative and integral) defined in the unit disk: , in a complex Banach space. Furthermore, a generalization of the admissible functions in complex Banach spaces is imposed, and applications are illustrated.
Rabha W. Ibrahim
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Generalized Hyers-Ulam Stability of a Mixed Type Functional Equation [PDF]

Abstract and Applied Analysis, 2013
Summary: We investigate the stability of a functional equation \(f(x+y+z)+f(x-y+z)+f(x+y-z)+f(-x+y+z)=3f(x)+f(-x)+3f(y)+f(-y)+3f(z)+f(-z)\) by applying the direct method in the sense of Hyers and Ulam.
Yang-Hi Lee, Soon-Mo Jung
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On the generalized Hyers-Ulam stability of Swiatak's functional equation [PDF]

Journal of Mathematical Inequalities, 2007
In this paper we shall study the generalized Hyers-Ulam stability of Swiatak's func- tional equation f (x + y )+ f (x − y )= 2f (x )+ 2f (y )+ g(x)g(y), x,y ∈ G, where G is an abelian group and f ,g : G −→ C are complex-valued functions satisfying the condition g(e) 0.
Bouikhalene Belaid, Elqorachi Elhoucien, Themistocles M. Rassias   +2 more
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Stability analysis and solutions of fractional boundary value problem on the cyclopentasilane graph [PDF]

Heliyon
The study is being applied to a model involving silane and on cyclopentasilane graph. We consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of cyclopentasilane. In this paper, we first study the existence of solutions to
Guotao Wang, Hualei Yuan, Dumitru Baleanu   +2 more
doaj   +2 more sources

Hyers–Ulam stability of a generalized Apollonius type quadratic mapping

Journal of Mathematical Analysis and Applications, 2006
The functional equation \[ Q(z-x)+Q(z-y)=\frac{1}{2}Q(x-y)+2Q \biggl(z-\frac{x+y}{2}\biggr), \] which was motivated by Apollonius' identity \(\|z-x\|^2+\|z-y\|^2=\frac{1}{2}\|x-y\|^2+2\|z-\frac{x+y}{2}\|^2\) in inner product spaces, is said to be the quadratic functional equation of Apollonius type.
Park, Chun-Gil, Rassias, Themistocles M.
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On Ulam–Hyers–Rassias stability of a generalized Caputo type multi-order boundary value problem with four-point mixed integro-derivative conditions [PDF]

Advances in Difference Equations, 2020
In this research article, we turn to studying the existence and different types of stability such as generalized Ulam–Hyers stability and generalized Ulam–Hyers–Rassias stability of solutions for a new modeling of a boundary value problem equipped with ...
Salim Ben Chikh, Abdelkader Amara, Sina Etemad, Shahram Rezapour   +3 more
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Generalized Linear Differential Equation using Hyers - Ulam Stability Approach

European Journal of Pure and Applied Mathematics
In this paper, We demonstrate the Hyers - Ulam stability of linear differential equation of fourth order. We interact with the differential equation\begin{align*}\gamma^{iv} (\omega) + \rho_1 \gamma{'''} (\omega)+ \rho_2 \gamma{''} (\omega) + \rho_3 \gamma' (\omega) + \rho_4 \gamma(\omega) = \chi(\omega),\end{align*}where $\gamma \in c^4 [\alpha,\beta],
S. Bowmiya, G. Balasubramanian, Vediyappan Govindan, Mana Donganont, Haewon Byeon   +4 more
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Existence, uniqueness and Ulam's stabilities for a class of implicit impulsive Langevin equation with Hilfer fractional derivatives

AIMS Mathematics, 2021
In this manuscript, a class of implicit impulsive Langevin equation with Hilfer fractional derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss existence, uniqueness,
Xiaoming Wang, Rizwan Rizwan , Jung Rey Lee, Akbar Zada , Syed Omar Shah   +4 more
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Generalized Hyers–Ulam Stability of the Additive Functional Equation [PDF]

Axioms, 2019
We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x2, … xn) + f(y1, y2, …, yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of ...
Yang-Hi Lee, Gwang Kim
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