• Korean Journal of Mathematics
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• v.22 no.1
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• pp.139-150
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• 2014

We introduce the concept of generalized (${\theta}$, ${\phi}$)-derivations on Banach algebras, and prove the Cauchy-Rassias stability of generalized (${\theta}$, ${\phi}$)-derivations on Banach algebras.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.263-274
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• 2006

In this paper, we prove the Hyers-Ulam-Rassias stability of the quadratic mapping in generalized quasi-Banach spaces, and of the quadratic mapping in generalized p-Banach spaces.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.401-410
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• 2002

We prove the generalized Hyers-Ulam-Rassias stability of generalized Jensen's functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with generalized Jensen's functional equations in Banach algebras.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.175-193
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• 2005

In [1], the concept of generalized (${\theta}$, ${\phi}$)-derivations on rings was introduced. In this paper, we introduce the concept of generalized (${\theta}$, ${\phi}$)-derivations on Poisson Banach algebras and of generalizd (${\theta}$, ${\phi}$)-derivations on Jordan Banach algebras, and prove the Cauchy-Rassias stability of generalized (${\theta}$, ${\phi}$)-derivations on Poisson Banach algebras and of generalized (${\theta}$, ${\phi}$)-derivations on Jordan Banach algebras.

• 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.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.345-351
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• 2005

An effective method for analyzing the stability of nonlinear systems is developed. After introducing a novel concept named the point- wise generalized Dahlquist constant for any mapping and presenting its useful properties, we show that the point-wise generalized Dahlquist constant is sufficient for characterizing the exponential stability of nonlinear systems.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.221-238
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• 2011

We prove the Hyers-Ulam stability of generalized Jensen's equations in Banach modules over a unital $C^{\ast}$-algebra. It is applied to show the stability of generalized Jensen's equations in a Hilbert module over a unital $C^{\ast}$-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital $C^{\ast}$-algebra.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.749-763
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• 2021

This research article deals with the Mittag-Leffler-Hyers-Ulam stability of linear and impulsive fractional order differential equation which involves the Caputo derivative. The application of the generalized fractional Fourier transform method and fixed point theorem, evaluates the existence, uniqueness and stability of solution that are acquired for the proposed non-linear problems on Lizorkin space. Finally, examples are introduced to validate the outcomes of main result.

• 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 Korean Data and Information Science Society
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• v.21 no.3
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• pp.597-603
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• 2010

We obtain, in using generalized norms, some stability results for a very general system of di erential equations using the method of cone-valued Lyapunov funtions and we obtain necessary and/or sufficient conditions for the uniformly asymptotic stability of the nonlinear differential system.