Results 1 to 10 of about 1,588 (206)
Approximation on the Quadratic Reciprocal Functional Equation [PDF]
Journal of Function Spaces, 2014 The quadratic reciprocal functional equation is introduced. The Ulam stability problem for an ϵ-quadratic reciprocal mapping f:X→Y between nonzero real numbers is solved.
Abasalt Bodaghi, Sang Og Kim
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A functional equation originating from quadratic forms
Journal of Mathematical Analysis and Applications, 2007 In this paper, we obtain the general solution and the stability of the 2-variable quadratic functional equationf(x+y,z+w)+f(x−y,z−w)=2f(x,z)+2f(y,w).
Jae-Hyeong Bae, Won-Gil Park
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Stability of the quadratic functional equation in Lipschitz spaces [PDF]
Journal of Mathematical Analysis and Applications, 2004 Let G be an Abelian group with a metric d and E a normed space. For any f:G→E we define the quadratic difference of the function f by the formula Qf(x,y):=2f(x)+2f(y)−f(x+y)−f(x−y) for x,y∈G.
Dłutek, K., Czerwik, S.
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The stability of the quadratic functional equation on amenable groups
Journal of Mathematical Analysis and Applications, 2004 All the literature on the stability of the quadratic functional equation focus on the case where the relevant domain is an Abelian group or a normed space.
Dilian Yang
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On the stability of a quadratic Jensen type functional equation
Journal of Mathematical Analysis and Applications, 2002 In this paper we obtain the general solution of the quadratic Jensen type functional equation 9fx+y+z3+f(x)+f(y)+f(z)=4fx+y2+fy+z2+fz+x2 and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and ...
Lee, Young Whan
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On approximation of approximately generalized quadratic functional equation via Lipschitz criteria
Quaestiones Mathematicae, 2019 Let G be an Abelian group with a metric d and E ba a normed space. For any f : G → E we define the generalized quadratic difference of the function f by the formulaQkf(x, y) := f(x + ky) + f(x - ky) - f(x + y) - f(x - y) - 2(k2 - 1) f(y)for all x, y ∈ G ...
Iz-Iddine El-Fassi
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Random stability and hyperstability of multi-quadratic mappings [PDF]
, 2022 In this paper, we introduce a new quadratic functional equation. In light of this equation, we define the multi-quadratic mappings and reduce the system of n equations defining the multi-quadratic mappings to a single equation.
Park, Choonkil +5 more
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Fuzzy Stability of Quadratic Functional Equations [PDF]
Advances in Difference Equations, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dong Yun Shin +3 more
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A Multidimensional Functional Equation Having Quadratic Forms as Solutions [PDF]
, 2007 We obtain the general solution and the stability of the -variable quadratic functional equation The quadratic form is a solution of the given functional equation.
Bae Jae-Hyeong +5 more
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Nonlinear stability of a quadratic functional equation with complex involution [PDF]
, 2011 summary:Let $X, Y$ be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping $f : X \rightarrow Y$ satisfies \begin{eqnarray} f(x+i y)+ f(x-iy) = 2 f(x) - 2f(y) \end{eqnarray} for all $x$, $y\in X$, then the mapping $f \colon X \
Saadati, Reza, Sadeghi, Ghadir
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