Stability of generalized quadratic functional equation on a set of measure zero
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2015 In this paper we prove the Hyers-Ulam stability of the following K-quadratic functional equation ∑ k ∈ K f(x+ k.y)= Lf(x)+ Lf(y), x,y ∈ E, where E is a real (or complex) vector space.
Youssef Aribou +3 more
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The Stability of a Quadratic Functional Equation with the Fixed Point Alternative
Abstract and Applied Analysis, 2009 Lee, An and Park introduced the quadratic functional equation f(2x+y)+f(2x−y)=8f(x)+2f(y) and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias.
Choonkil Park, Ji-Hye Kim
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Monotonic solutions of functional integral and differential equations of fractional order [PDF]
, 2009 The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equations have been studied by J. Banas. Here we are concerned with a singular quadratic functional integral equations.
El-Sayed, Ahmed, Hashem, H.H.G.
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Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications * [PDF]
, 2016 We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes with respect to ...
Pham, Huyên
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Intuitionistic Fuzzy Stability of a Quadratic Functional Equation
Fixed Point Theory and Applications, 2010 We consider the intuitionistic fuzzy stability of the quadratic functional equation by using the fixed point alternative, where is a positive integer.
Wang Liguang
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ORTHOGONALLY ADDITIVE AND ORTHOGONALLY QUADRATIC FUNCTIONAL EQUATION [PDF]
Korean Journal of Mathematics, 2013 Summary: Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation \[ \begin{multlined} f\left(\frac{x}{2}+y\right) + f\left(\frac{x}{2}-y\right) + f\left(\frac{x}{2}+z\right) + f\left(\frac{x}{2}-z\right) \\ = 3f(x) - 1 f (- x) + f(y) + f (- y) + f(z) + f (- z) \end ...
Lee, Jung Rye +2 more
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A General Uniqueness Theorem concerning the Stability of Additive and Quadratic Functional Equations
Journal of Function Spaces, 2015 We prove a general uniqueness theorem that can be easily applied to the (generalized) Hyers-Ulam stability of the Cauchy additive functional equation, the quadratic functional equation, and the quadratic-additive type functional equations.
Yang-Hi Lee, Soon-Mo Jung
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Mathematics, 2019 The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation. In this paper, we investigate Hyers−Ulam&
Yang-Hi Lee
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On analytical solutions of f(R) modified gravity theories in FLRW cosmologies [PDF]
, 2013 A novel analytical method for f(R) modified theories without matter in Friedmann-Lemaitre-Robertson-Walker spacetimes is introduced. The equation of motion for the scale factor in terms of cosmic time is reduced to the equation for the evolution of the ...
Appleby S. A. +13 more
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On the Stability of Quadratic Functional Equations in F-Spaces
Journal of Function Spaces, 2016 The Hyers-Ulam-Rassias stability of quadratic functional equation f(2x+y)+f(2x-y)=f(x+y)+f(x-y)+6f(x) and orthogonal stability of the Pexiderized quadratic functional equation f(x+y)+f(x-y)=2g(x)+2h(y) in F-spaces are proved.
Xiuzhong Yang
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