• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.419-433
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• 2013

In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of functional equations, called general system of nonlinear functional equations, in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.445-453
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• 2007

This paper deals with the approximate controllability for the nonlinear functional differential equations with time delay and studies a variation of constant formula for solutions of the given equations.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.57-79
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• 2023

We investigate the existence and uniform attractivity of solutions of a class of functional integral equations which contain a number of classical nonlinear integral equations as special cases. Using the technique of measures of noncompactness and a fixed point theorem of Darbo type we prove the existence of solutions of these equations in the Banach space of continuous and bounded functions on the nonnegative real half axis. Our results extend and improve some known results in the recent literature. An example illustrating the main result is presented in the last section.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.1-14
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• 2018

In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.865-876
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• 2023

This paper presents properties of the cocycle equations via cochains on a semigroup. And then we offer hyperstability results of related functional equations using the properties of cocycle equations via cochains. These results generalize hyperstability results of a class of linear functional equation by Maksa and Páles. The obtained results can be applied to obtain hyperstability of various functional equations such as Euler-Lagrange type quadratic equations.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.3
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• pp.315-321
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• 1988

The input-output relation for nonlinear systems can e explicitly represented by the volterra functional series and it is characterized by the Volterra kernels. A block diagram reduction method is proposed to determine the Volterra kernels for nonlinear differential equations and is compared with the direct substitution techniques. The former method can significantly reduce the computational complexity. A degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.8
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• pp.726-730
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• 2001

In this paper, we consider the observability conditions for the following nonlinear fuzzy neutral functional differential equations in E$^{2}$$_{N}$.

• East Asian mathematical journal
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• v.14 no.2
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• pp.299-309
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• 1998

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.635-643
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• 2002

The asymptotic behaviour of the solutions of initial - boundary value problem for a class of nonlinear parabolic differential - functional equations is studied via the method of differential inequalities in order to obtain oscillation criterion for the solutions.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.173-181
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• 2012

In this paper, we study the control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under the Lipschitz continuity condition of the nonlinear term, we can obtain the sufficient conditions for the approximate controllability of nonlinear functional equations with nonlinear monotone hemicontinuous and coercive operator. The existence, uniqueness and a variation of solutions of the system are also given.