Results 51 to 60 of about 29,994 (153)
On a functional equation originating from a mixed additive and cubic equation and its stability
Hacettepe Journal of Mathematics and Statistics, 2015 In this paper, we study solutions of the 2-variable mixed additive andcubic functional equationf (2x + y, 2z + t) + f (2x − y, 2z − t) = 2f (x + y, z + t)+ 2f (x − y, z − t) + 2f (2x, 2z) − 4f (x, z),which has the cubic form f (x, y) = ax+ bx y + cxy+ dy as a solution.
JANFADA, Mohammad +2 more
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Cubic Functional Equations on Restricted Domains of Lebesgue Measure Zero
Canadian Mathematical Bulletin, 2017 AbstractLet X be a real normed space, Y a Banach space, and f : X → Y. We prove theUlam–Hyers stability theorem for the cubic functional equationin restricted domains. As an application we consider a measure zero stability problem of the inequalityfor all (x, y) in Γ ⸦ ℝ2 of Lebesgue measure 0.
Choi, C.-K. +3 more
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A Note to Paper "On the Stability of Cubic Mappings and Quartic Mappings in Random Normed Spaces"
Journal of Inequalities and Applications, 2009 Recently, Baktash et al. (2008) proved the stability of the cubic functional equation and the quartic functional equation in random normed spaces. In this note, we correct the proofs.
Cho YJ, Saadati R, Vaezpour SM
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Solution and Stability of a Mixed Type Cubic and Quartic Functional Equation in Quasi-Banach Spaces
Abstract and Applied Analysis, 2009 We obtain the general solution and the generalized Ulam-Hyers stability of the mixed type cubic and quartic functional equation f(x+2y)+f(x−2y)=4(f(x+y)+f(x−y))−24f(y)−6f(x)+3f(2y) in quasi-Banach spaces.
M. Eshaghi Gordji +3 more
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Nonlinear Random Stability via Fixed-Point Method
Journal of Applied Mathematics, 2012 We prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y) in various complete random normed spaces.
Yeol Je Cho, Shin Min Kang, Reza Saadati
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Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces
Abstract and Applied Analysis, 2010 Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y) in non-Archimedean Banach spaces.
Choonkil Park
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On asymptotic behaviors of a specific cubic functional equation and its hyperstability
Demonstratio MathematicaIn this article, the asymptotic behavior and hyperstability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) $$f\left(2x+y\right)+f\left(2x-y\right)=2f\left(x+y\right)+2f\left(x-y\right)+12f\left(x\right)$$ are discussed.
Bae Jae-Hyeong +2 more
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Journal of Taibah University for ScienceIn the field of functional equations and their solutions, Ulam's stability is an essential concept. This theory examines whether the function approximating a certain functional equation is close to the function that exactly satisfies it.
Ramakrishnan Kalaichelvan +5 more
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Journal of MathematicsIn the current study, we introduce a system of functional equations (FEs) deriving from the mixed type additive–quadratic and the mixed-type cubic–quartic FEs which describes a multimixed additive–quadratic–cubic–quartic mapping.
Siriluk Donganont, Abasalt Bodaghi
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Fuzzy Stability of Generalized Mixed Type Cubic, Quadratic, and Additive Functional Equation
Journal of Inequalities and Applications, 2011 In this paper, we prove the generalized Hyers-Ulam stability of generalized mixed type cubic, quadratic, and additive functional equation, in fuzzy Banach spaces. 2010 Mathematics Subject Classification: 39B82; 39B52.
Shin Dong +4 more
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