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1
Content available remote Stability of an additive-quadratic-quartic functional equation
Kim Gwang Hui, Lee Yang-Hi
Demonstratio Mathematica
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2020
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Vol. 53, nr 1
1--7
EN
In this paper, we investigate the stability of an additive-quadratic-quartic functional equation f(x+2y)+f(x-2y) - 2f(x+y) - 2f(-x-y) - 2f(x-y) - 2f(y-x)+4f(-x)+2f(x) - f(2y) - f(-2y)+4f(y)+4f(-y)=0 by the direct method in the sense of Găvruta.
2
Content available remote Hyers-Ulam stability of a nonautonomous semilinear equation with fractional diffusion
Villa-Morales José
Demonstratio Mathematica
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2020
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Vol. 53, nr 1
269--276
EN
In this paper, we study the Hyers-Ulam stability of a nonautonomous semilinear reaction-diffusion equation. More precisely, we consider a nonautonomous parabolic equation with a diffusion given by the fractional Laplacian. We see that such a stability is a consequence of a Gronwall-type inequality.
3
Content available remote Hyers-Ulam stability of quadratic forms in 2-normed spaces
Park Won-Gil, Bae Jae-Hyeong
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
496--502
EN
In this paper, we obtain Hyers-Ulam stability of the functional equations f(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) and f(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.
4
Content available remote Hyers-Ulam stability of a coupled system of fractional differential equations of Hilfer-Hadamard type
Ahmad Manzoor, Zada Akbar, Alzabut Jehad
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
283--295
EN
In this paper, existence and uniqueness of solution for a coupled impulsive Hilfer-Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers-Ulam stability are also discussed. We provide an example demonstrating consistency to the theoretical findings.
5
Content available remote Existence and stability of impulsive coupled system of fractional integrodifferential equations
Zada Akbar, Waheed Hira, Alzabut Jehad, Wang Xiaoming
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
296--335
EN
In this manuscript, we deal with a class and coupled system of implicit fractional differential equations, having some initial and impulsive conditions. Existence and uniqueness results are obtained by means of Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. Hyers–Ulam stability is investigated by using classical technique of nonlinear functional analysis. Finally, we provide illustrative examples to support our obtained results.
6
Approximately linear recurrences
Rasouli H., Abbaszadeh S., Eshaghi M.
Journal of Applied Analysis
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2018
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Vol. 24, nr 1
81--85
EN
In this paper, we present a Hyers–Ulam stability result for the approximately linear recurrence in Banach spaces. An example is given to show the results in more tangible form.
7
Content available remote Stability and hyperstability of a quadratic functional equation and a characterization of inner product spaces
EL-Fassi I., Park C., Kim G. H.
Demonstratio Mathematica
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2018
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Vol. 51, nr 1
295--303
EN
We have proved the Hyers-Ulam stability and the hyperstability of the quadratic functional equation f(x+y+z) +f(x+y−z) +f(x−y+z) +f(−x+y+z) = 4[f(x) +f(y) +f(z) ] in the class of functions from an abelian group G into a Banach space.
8
Content available remote Orthogonal stability of mixed type additive-cubic functional equations in multi-Banach spaces
Murali R., Pinelas S., Raj A. A.
Demonstratio Mathematica
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2018
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Vol. 51, nr 1
106--111
EN
In this paper, we establish the Hyers-Ulam orthogonal stability of the mixed type additive-cubic functional equation in multi-Banach spaces.
9
Content available remote On the stability of a Cauchy type functional equation
Najati A., Lee J. R., Park C., Rassias T. M.
Demonstratio Mathematica
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2018
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Vol. 51, nr 1
323--331
EN
In this work, the Hyers-Ulam type stability and the hyperstability of the functional equation [wzór] are proved.
10
Content available remote Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales
Anderson D. R., Onitsuka M.
Demonstratio Mathematica
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2018
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Vol. 51, nr 1
198--210
EN
We establish the Hyers-Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, which include the continuous (step size zero) and the discrete (step size constant and nonzero) dynamic equations as important special cases. In particular, for certain parameter values in relation to the graininess of the time scale, we find the minimum HUS constants. A few nontrivial examples are provided. Moreover, an application to a perturbed linear dynamic equation is also included.
11
Content available remote Intuitionistic fuzzy almost Cauchy–Jensen mappings
Gordji M. E., Abbaszadeh S.
Demonstratio Mathematica
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2016
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Vol. 49, nr 1
18--25
EN
In this paper, we first investigate the Hyers–Ulam stability of the generalized Cauchy–Jensen functional equation of p-variable (…) in an intuitionistic fuzzy Banach space. Then, we conclude the results for Cauchy–Jensen functional equation of p-variable (…). Next, we discuss the intuitionistic fuzzy continuity of Cauchy–Jensen mappings.
12
Content available Note on the stability of first order linear differential equations
Bojor F.
Opuscula Mathematica
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2012
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Vol. 32, no. 1
67-74
EN
In this paper, we will prove the generalized Hyers-Ulam stability of the linear differential equation of the form y'(x)+f (x) y(x)+g(x) = 0 under some additional conditions.
13
Content available remote A note on stability of the popoviciu functional equation on restricted domain
Brzdęk J.
Demonstratio Mathematica
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2010
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Vol. 43, nr 3
635-641
EN
We prove the Hyers-Ulam stability, on restricted domain, of a functional equation of Jensen type, introduced by T. Popoviciu (1965).
14
Content available remote On Hyers-Ulam stability of the Pexider equation
Kominek Z.
Demonstratio Mathematica
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2004
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Vol. 37, nr 2
373--376
15
Content available remote Stability of the homogeneous equation
Chudziak J.
Demonstratio Mathematica
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1998
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Vol. 31, nr 4
765-772
EN
The problem of Hyers-Ulam stability of the homogeneous equation is considered. We show , that under suitable assumptions on p and q, every function satisfying (4) is homogeneous.
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