• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.720-723
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• 1999

For that the attitude control performance test of the satellite, dynamic analysis of satellite structure performed in reference with KOREASAT, and the equation of motion of rigid bodies was derivated. For attitude stability, Lyapunov's stability theorem and state space expression were applied to dynamic equation of satellite. To prove efficiency of our method, simulations are performed and result are shown.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.479-487
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• 2007

A variety of Feynman's operational calculus for noncommuting operators was studied [3,4,5,6,7,10]. And a stability in the continuous measures for Feynman's operational calculus was studied [9]. In this paper, we investigate a stability of the Feynman's operational calculus in the setting where the time-ordering measures are allowed to have both continuous and discrete parts.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.691-700
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• 2009

We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.453-464
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• 2016

In this paper, we investigate the solution of the following functional inequality $$N(f(x)+f(y)+f(z),t){\geq}N(f(x+y+z),mt)$$ for some fixed real number m with $\frac{1}{3}$ < m ${\leq}$ 1 and using the fixed point method, we prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.313-328
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• 2011

We investigate the stability of the functional equation f(x+y+z+w)+2f(x)+2f(y)+2f(z)+2f(w)-f(x+y)-f(x+z)-f(x+w)-f(y+z)-f(y+w)-f(z+w)=0 by using a flxed point theorem in the sense of L. C$\breve{a}$adariu and V. Radu.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.163-175
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• 2020

The stability of a class of Volterra-type difference equations that include a generalized difference operator ∆_a is investigated using Krasnoselskii's fixed point theorem and some results are obtained. In addition, some examples are given to illustrate our theoretical results.

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.297-306
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• 2009

In this paper, we obtain the general solution and the generalized HyersUlam stability theorem for an additive functional equation $af(x+y)+2f({\frac{x}{2}}+y)+2f(x+{\frac{y}{2})=(a+3)[f(x)+f(y)]$for any fixed integer a.

• The Pure and Applied Mathematics
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• v.26 no.2
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• pp.85-97
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• 2019

In this paper we introduce the reciprocal-negative Fermat's equation induced by the famous equation in the Fermat's Last Theorem, establish the general solution in the simplest cases and the differential solution to the equation, and investigate, then, the generalized Hyers-Ulam stability in a $quasi-{\beta}-normed$ space with both the direct estimation method and the fixed point approach.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.801-812
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• 2022

In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers-Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1089-1103
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• 2022

This paper focuses on the existence and uniqueness outcome for fractional integro-differential equation (FIDE) among impulsive edge condition and Hyers-Ulam-Rassias Stability (HURS) by using fractional calculus and some fixed point theorem in some weak conditions. The outcome procured in this paper upgrade and perpetuate some studied solutions.