The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Choonkil Park - One of the best experts on this subject based on the ideXlab platform.
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c c algebra valued fuzzy normed spaces with application of hyers ulam Stability of a random integral equation
Advances in Difference Equations, 2020Co-Authors: Reza Chaharpashlou, Choonkil Park, Donal Oregan, Reza SaadatiAbstract:In this paper, we consider $C^{*}$ -algebra valued fuzzy normed spaces. We study the random integral equation $(\frac{1}{2c})\int _{x-cd}^{x+cd}u(\gamma ,\tau ,d_{0})\,d\tau =u( \gamma ,x,d)$ which is related to the stochastic wave equation. In addition, using a $C^{*}$ -algebra valued fuzzy controller function, we consider its $C^{*}$ -algebra valued fuzzy Hyers–Ulam Stability.
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on approximate solution of lattice functional equations in banach f algebras
Math 2020 Vol. 5 Pages 5458-5469, 2020Co-Authors: Ehsan Movahednia, Choonkil Park, Young Cho, Siriluk PaokantaAbstract:The aim of the current manuscript is to prove the Hyers-Ulam Stability of supremum, infimum and multiplication preserving functional equations in Banach f -algebras. In fact, by using the direct method and the fixed point method, the Hyers-Ulam Stability of the functional equations is proved.
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ulam s type Stability of higher order nonlinear delay differential equations via integral inequality of gronwall bellman bihari s type
Applied Mathematics and Computation, 2019Co-Authors: Akbar Zada, Choonkil ParkAbstract:Abstract In this paper, we prove the Hyers-Ulam Stability and the Hyers-Ulam-Rassias Stability of a class of higher order nonlinear delay differential equations with multiple bounded variable delays on a compact interval. Result of existence and uniqueness of solution is obtained by fixed point approach. Meanwhile, for the first time, integral inequality of Gronwall-Bellman-Bihari’s type with delay is applied to prove the Stability theorem which made our results more generalized and interesting.
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bi additive s functional inequalities and quasi multipliers on banach algebras
Bulletin of the Brazilian Mathematical Society New Series, 2019Co-Authors: Choonkil ParkAbstract:In this paper, we solve the following bi-additive s-functional inequalities where s is a fixed nonzero complex number with $$|s |< 1$$ , and where s is a fixed nonzero complex number with $$|s |< 1$$ . Moreover, we prove the Hyers–Ulam Stability of quasi- $$*$$ -multipliers on Banach $$*$$ -algebras and unital $$C^*$$ -algebras, associated with the bi-additive s-functional inequalities (1) and (2).
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additive s functional inequality and hom derivations in banach algebras
Journal of Fixed Point Theory and Applications, 2019Co-Authors: Choonkil Park, Xiaohong ZhangAbstract:In this paper, we introduce and solve the following additive s-functional inequality: 0.1 $$\begin{aligned} \left\| f\left( x+y\right) - f(x )- f(y)\right\| \le \Vert s (f(x-y)-f(x)-f(-y))\Vert , \end{aligned}$$ where s is a fixed nonzero complex number with $$|s|<1$$ . Using the fixed point method and the direct method, we prove the Hyers–Ulam Stability of the additive s-functional inequality (0.1) in complex Banach spaces. Furthermore, we prove the Hyers–Ulam Stability of hom-derivations in complex Banach algebras.
Soonmo Jung - One of the best experts on this subject based on the ideXlab platform.
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a fixed point approach to the Stability of a mean value type functional equation
Mathematics, 2017Co-Authors: Soonmo Jung, Yanghi LeeAbstract:We prove the generalized Hyers–Ulam Stability of a mean value type functional equation f ( x ) − g ( y ) = ( x − y ) h ( x + y ) by applying a method originated from fixed point theory.
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on the Stability of the linear functional equation in a single variable on complete metric groups
arXiv: Functional Analysis, 2015Co-Authors: Soonmo Jung, Dorian Popa, Michael Th. RassiasAbstract:In this paper we obtain a result on Hyers-Ulam Stability of the linear functional equation in a single variable $f(\varphi(x)) = g(x) \cdot f(x)$ on a complete metric group.
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hyers ulam Stability of the first order matrix difference equations
Journal of Function Spaces and Applications, 2015Co-Authors: Soonmo JungAbstract:We prove the generalized Hyers-Ulam Stability of the first-order linear homogeneous matrix differential equations . Moreover, we apply this result to prove the generalized Hyers-Ulam Stability of the th order linear differential equations with variable coefficients.
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hyers ulam Stability of the first order matrix difference equations
Advances in Difference Equations, 2015Co-Authors: Soonmo JungAbstract:In this paper, we prove the Hyers-Ulam Stability of the first-order linear homogeneous matrix difference equations $\vec{x}_{i} = \mathbf{A} \vec{x}_{i-1}$ and $\vec{x}_{i-1} = \mathbf{A} \vec{x}_{i}$ for all integers $i \in\mathbf{Z}$ .
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the inhomogeneous euler equation and its hyers ulam Stability
Applied Mathematics Letters, 2015Co-Authors: Cristinel Mortici, Themistocles M Rassias, Soonmo JungAbstract:Abstract In this paper, we solve the inhomogeneous Euler differential equation, x 2 y ″ ( x ) + α x y ′ ( x ) + β y ( x ) = f ( x ) , and prove the Hyers–Ulam Stability of that equation on a bounded domain by using the integration method. Our results extend the results of Jung and Min (2009).
John Michael Rassias - One of the best experts on this subject based on the ideXlab platform.
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Stability of euler lagrange jensen s a b sextic functional equation in multi banach spaces
International Journal of Analysis and Applications, 2018Co-Authors: John Michael Rassias, R Murali, Antony A RajAbstract:In this paper, we prove the Hyers-Ulam Stability of Euler-Lagrange-Jensen’s (a,b)-Sextic Functional Equation in Multi-Banach Spaces.
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quadratic functional equations in a set of lebesgue measure zero
Journal of Mathematical Analysis and Applications, 2014Co-Authors: Jaeyoung Chung, John Michael RassiasAbstract:Abstract Let R be the set of real numbers, Y a Banach space and f : R → Y . We prove the Hyers–Ulam Stability theorem for the quadratic functional inequality ‖ f ( x + y ) + f ( x − y ) − 2 f ( x ) − 2 f ( y ) ‖ ≤ ϵ for all ( x , y ) ∈ Ω , where Ω ⊂ R 2 is of Lebesgue measure 0. Using the same method we dealt with the Stability of two more functional equations in a set of Lebesgue measure 0.
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a fixed point approach to the Stability of an aq functional equation on β banach modules
Fixed Point Theory and Applications, 2012Co-Authors: John Michael RassiasAbstract:Using the fixed point method, we prove the Hyers-Ulam Stability of the following mixed additive and quadratic functional equation f (kx + y) + f(kx - y) = f(x + y) + f(x - y) + (k - 1) [(k + 2) f(x) + kf(-x)] (k ∈ ℕ, k ≠ 1) in β-Banach modules on a Banach algebra.
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generalized ulam hyers Stability of a general mixed aqcq functional equation in multi banach spaces a fixed point approach
European Journal of Pure and Applied Mathematics, 2010Co-Authors: John Michael RassiasAbstract:Using the fixed point method, we investigate the generalized Hyers-Ulam Stability of the general mixed additive-quadratic-cubic-quartic functional equation in multi-Banach spaces.
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a fixed point approach to the Stability of a general mixed aqcq functional equation in non archimedean normed spaces
Discrete Dynamics in Nature and Society, 2010Co-Authors: John Michael RassiasAbstract:Using the fixed point methods, we prove the generalized Hyers-Ulam Stability of the general mixed additive-quadratic-cubic-quartic functional equation (
Dorian Popa - One of the best experts on this subject based on the ideXlab platform.
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hyers ulam Stability with respect to gauges
Journal of Mathematical Analysis and Applications, 2017Co-Authors: Janusz Brzdek, Dorian Popa, Ioan RasaAbstract:Abstract We suggest a somewhat new approach to the issue of Hyers–Ulam Stability. Namely, let A, B be (real or complex) linear spaces, L : A → B be a linear operator, N : = k e r L , and ρ A and ρ B be semigauges on A and B, respectively. We say that L is HU-stable with constant K ≥ 0 if for each x ∈ A such that ρ B ( L x ) ≤ 1 there exists z ∈ N with ρ A ( z − x ) ≤ K . With that definition we obtain quite general outcomes concerning approximate solutions to some differential equations.
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on the Stability of the linear functional equation in a single variable on complete metric groups
arXiv: Functional Analysis, 2015Co-Authors: Soonmo Jung, Dorian Popa, Michael Th. RassiasAbstract:In this paper we obtain a result on Hyers-Ulam Stability of the linear functional equation in a single variable $f(\varphi(x)) = g(x) \cdot f(x)$ on a complete metric group.
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on the Stability of some classical operators from approximation theory
Expositiones Mathematicae, 2013Co-Authors: Dorian Popa, Ioan RasaAbstract:Abstract We obtain some results on Hyers–Ulam Stability for some classical operators from approximation theory. For Bernstein operators we determine the Hyers–Ulam constant using a result concerning coefficient bounds of Lorentz representation for a polynomial.
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hyers ulam Stability of the linear differential operator with nonconstant coefficients
Applied Mathematics and Computation, 2012Co-Authors: Dorian Popa, Ioan RasaAbstract:Abstract We obtain some Stability results for the linear differential operator of order one in Banach spaces. As a consequence we derive a result on Hyers–Ulam Stability for the linear differential operator of higher order with nonconstant coefficients.
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hyers ulam Stability of a first order partial differential equation
Journal of Mathematical Analysis and Applications, 2012Co-Authors: Nicolaie Lungu, Dorian PopaAbstract:Abstract We prove that the existence of a global prime integral leads, in appropriate conditions, to the Hyers–Ulam Stability of a linear partial differential equation of first order.
Jihye Kim - One of the best experts on this subject based on the ideXlab platform.
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a fixed point approach to the Stability of an additive quadratic cubic quartic functional equation
Fixed Point Theory and Applications, 2010Co-Authors: Jung Rye Lee, Jihye Kim, Choonkil ParkAbstract:Using the fixed point method, we prove the generalized Hyers-Ulam Stability of the following additive-quadratic-cubic-quartic functional equation Open image in new window in Banach spaces.
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the Stability of a quadratic functional equation with the fixed point alternative
Abstract and Applied Analysis, 2009Co-Authors: Choonkil Park, Jihye KimAbstract:Lee, An and Park introduced the quadratic functional equation and proved the Stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam Stability of the quadratic functional equation in Banach spaces.