• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.325-336
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• 2001

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of a quadratic function equation f(x+y+z)+f(x-y)+f(y-z)+f(z-x)=3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam-Rassias stability of the equation on bounded domain.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.825-840
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• 2007

In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.607-619
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• 2001

Rassias obtained the Hyers-Ulam stability of the gen-eral Euler-Lagrange functional equation. In this paper we general-ized this stability in the spirit of Hyers, Ulam, Rassias and Gavruta.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2061-2070
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• 2013

In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation $$2\sum_{j=1}^{n}f(\frac{x_j}{2}+\sum_{i=1,i{\neq}j}^{n}\;x_i)+\sum_{j=1}^{n}f(x_j)=2nf(\sum_{j=1}^{n}x_j)$$, in quasi-${\beta}$-normed spaces.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.165-174
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• 2008

In this paper, we obtain the general solution, the generalized Hyers-Ulam-Rassias stability, and the stability by using the alternative fixed point for a cubic functional equation $4f(x+my)+4f(x-my)+m^2f(2x)=8f(x)+4m^2f(x+y)+4m^2f(x-y)$ for a positive integer $m{\geq}2$.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.581-590
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• 2001

In this paper we prove a local stability of Gavruta’s theorem for the generalized Hyers-Ulam-Rassias Stability of Cauchy functional equation.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.165-177
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• 2024

In this paper, we investigate the suitable conditions for the existence results for a class of 𝔍-Hilfer fractional nonlinear Fredholm-Volterra models with new conditions. The findings are based on Banach contraction principle and Schauder's fixed point theorem. Also, the generalized Hyers-Ulam stability and generalized Hyers-Ulam-Rassias stability for solutions of the given problem are provided.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.515-523
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• 2007

In this paper, we investigate the Hyers-Ulam-Rassias stability of generalized Jensen type quadratic functional equations in Banach spaces.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.197-223
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• 2021

In this paper, we investigate existence, uniqueness and four different types of Ulam's stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and $Krasnosel^{\prime}ski{\breve{i}}{^{\prime}}s$ fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.45-50
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• 2000

The modified Hyers-Ulam-Rassias Stability Of the generalized form g(x+p) : $\phi$(x)g(x) for the Gamma functional equation shall be proved. As a consequence we obtain the stability theorems for the gamma functional equation.