Results 11 to 20 of about 456,013 (364)
Fuzzy Stability of a Quadratic-Additive Functional Equation [PDF]
International Journal of Mathematics and Mathematical Sciences, 2011 We investigate a fuzzy version of stability for 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.
Sun Sook Jin, Yang Hi Lee
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On the Stability of Quadratic Functional Equations [PDF]
Abstract and Applied Analysis, 2008 Let X, Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx + y) + f(kx-y) = 2k2f(x) + 2f(y) for all x, y ∈ X if and only if the mapping f : X → Y satisfies f(x + y) + f(x-y) = 2f(x) + 2f(y) for all x, y ∈ X. Furthermore, the Hyers‐Ulam‐Rassias stability of the above functional equation in Banach spaces is proven.
Jung Rye Lee, Jong Su An, Choonkil Park
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AIMS Mathematics, 2020 In this paper, we introduce a mixed type finite variable functional equation deriving from quadratic and additive functions and obtain the general solution of the functional equation and investigate the Hyers-Ulam stability for the functional equation in
K. Tamilvanan +2 more
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Random Stability of Quadratic Functional Equations
JOURNAL OF ADVANCES IN PHYSICS, 2019 In this paper, we investigate the generalized Hyers-Ulam stability on random -normed spaces associated with the following generalized quadratic functional equation ,where is a fixed positive integer via two ...
Mee Kwang Kang
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Mathematics, 2021 In this paper, the authors investigate the Hyers–Ulam stability results of the quadratic functional equation in Banach spaces and non-Archimedean Banach spaces by utilizing two different techniques in terms of direct and fixed point techniques.
K. Tamilvanan +3 more
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Characterization and stability analysis of advanced multi-quadratic functional equations
Advances in Difference Equations, 2021 In this paper, we introduce a new quadratic functional equation and, motivated by this equation, we investigate n-variables mappings which are quadratic in each variable.
Abasalt Bodaghi +2 more
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Characterization and Stability of Multi-Euler-Lagrange Quadratic Functional Equations
Journal of Function Spaces, 2022 The aim of the current article is to characterize and to prove the stability of multi-Euler-Lagrange quadratic mappings. In other words, it reduces a system of equations defining the multi-Euler-Lagrange quadratic mappings to an equation, say, the multi ...
Abasalt Bodaghi +2 more
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Ulam stability of an additive-quadratic functional equation in Banach spaces
Journal of Mathematical Inequalities, 2020 Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation f (x+ y,z+w)+ f (x− y,z−w)−2 f (x,z)−2 f (x,w) = 0.
I. Hwang, Choonkill Park
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Fuzzy normed spaces and stability of a generalized quadratic functional equation
AIMS Mathematics, 2020 In this paper, we acquire the general solution of the generalized quadratic functional equation \[ \begin{aligned} \sum_{1 \leq a < b < c \leq m}\varphi\left(r_{a}+r_{b}+r_{c}\right)&=(m-2)\sum_{1\leq a < b\leq m}\varphi\left(r_{a}+r_{b}\right) \\ &\quad-
Choonkill Park +4 more
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International Journal of Mathematics and Mathematical Sciences, 2023 In this manuscript, we study the properties and equivalence results for different forms of quadratic functional equations. Using the Brzdȩk and Ciepliński fixed-point approach, we investigate the generalized Hyers–Ulam–Rassias stability for the 3 ...
Ravinder Kumar Sharma, Sumit Chandok
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