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Stability of a Bi-Jensen Functional Equation on Restricted Unbounded Domains and Some Asymptotic Behaviors [PDF]
Mathematics, 2022 In this paper, we give some properties of the bi-Jensen functional equation and investigate its Hyers–Ulam stability and hyperstability. We construct a function which is bi-Jensen and is not continuous.
Jae-Hyeong Bae +2 more
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Stability of the multi-Jensen equation [PDF]
Journal of Mathematical Analysis and Applications, 2010 Let \(V\) and \(W\) denote normed spaces. A function \(f:V^m\to W\) is called multi-Jensen, if it satisfies the Jensen functional equation in each of its variables. It is well-known [see \textit{W. Prager} and \textit{J. Schwaiger}, Bull. Korean Math. Soc.
Krzysztof Cieplinski
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Intuitionistic fuzzy almost Cauchy–Jensen mappings [PDF]
Demonstratio Mathematica, 2016 In this paper, we first investigate the Hyers–Ulam stability of the generalized Cauchy–Jensen functional equation of p-variable f(∑i=1paixi)=∑i=1paif(xi)$f\left(\sum\nolimits_{i = 1}^p {a_i x_i } \right) = \sum\nolimits_{i = 1}^p {a_i f(x_i )}$ in an ...
Gordji M. E., Abbaszadeh S.
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On a Cubic Equation and a Jensen-Quadratic Equation [PDF]
Abstract and Applied Analysis, 2007 We obtain the general solutions of the cubic functional equation3[g(x+y)+g(x−y)+6g(x)]=2g(2x+y)+2g(2x−y)+g(−x−y)+g(−x+y)+6g(−x)and the Jensen-quadratic functional equationf((x+y)/2,z+w)+f((x+y)/2,z−w)=f(x,z)+f(x,w)+f(y,z)+f(y,w).
Jae-Hyeong Bae, Won-Gil Park
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STABILITY OF THE MULTI-JENSEN EQUATION [PDF]
Bulletin of the Korean Mathematical Society, 2008 A function \(f: V^m\to W\) (with \(V\) and \(W\) being vector spaces over \(\mathbb{Q}\) and a positive integer \(m\)) is called \textit{multi-Jensen} if for each of its \(m\) arguments it satisfies the Jensen equation \(F\left(\frac{x+y}{2}\right)=\frac{F(x)+F(y)}{2}\).
Wolfgang Prager, Jens Schwaiger
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On the stability of Jensen’s functional equation on groups [PDF]
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2007 In this paper we establish the stability of Jensen's functional equation on some classes of groups. We prove that Jensen equation is stable on noncommutative groups such as metabelian groups and $T(2, K)$, where $K$ is an arbitrary commutative field with characteristic different from two. We also prove that any group $A$ can be embedded into some group
Sahoo Prasanna K
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ON THE JENSEN’S EQUATION IN BANACH MODULES
Taiwanese Journal of Mathematics, 2002 \textit{Y.-H. Lee} and \textit{K.-W. Jun} [J. Math. Anal. Appl. 238, 305--315 (1999; Zbl 0933.39053)] proved the following Theorem: Let \(X\) be a Banach space, \(G\) be an Abelian group and~\(E\) be a~subset of \(G\) such that \(nx\in E\) for any integer~\(n\) and for all \(x\in E\) and \(2x\neq 0\), \(3x\neq 0\) for all \(x\in E\setminus\{0\}\). Let \
Won-Gil Park, Chun-Gil Park
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A Variant of Jensen’s Functional Equation on Semigroups
Demonstratio Mathematica, 2016 Abstract We determine the solutions f : S → H of the following functional equation f(xy) + f(σ(y)x) = 2f(x); x; y ∈ S; and the solutions f1; f2; f3 : M → H of the functional equation f1(xy) + f2(σ(y)x) = 2f31(x); x; y ∈ M; where S is a semigroup, M is a monoid, H is an abelian ...
Samir Kabbaj, Driss Zeglami
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Set-valued solutions for an equation of Jensen type
Journal of Numerical Analysis and Approximation Theory, 1999 Not available.
Dorian Popa
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Fuzzy Optimization and Modeling, 2022 In present paper, the stability of generalized Jordan derivations associated with Hochschild 2-cocycles of triangular algebras for the generalized kind of Jensen-type functional equation is investigated.
Rohollah Bakhshandeh, Isa Bakhshandeh
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