A Fixed Point Approach to the Stability of a Cauchy-Jensen Functional Equation [PDF]
Abstract and Applied Analysis, 2012 We find out the general solution of a generalized Cauchy-Jensen functional equation and prove its stability. In fact, we investigate the existence of a Cauchy-Jensen mapping related to the generalized Cauchy-Jensen functional equation and prove its ...
Jae-Hyeong Bae, Won-Gil Park
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The Jensen functional equation in non-Archimedean normed spaces [PDF]
Journal of Function Spaces and Applications, 2009 We investigate the Hyers–Ulam–Rassias stability of the Jensen functional equation in non-Archimedean normed spaces and study its asymptotic behavior in two directions: bounded and unbounded Jensen differences.
Mohammad Sal Moslehian
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On Approximation Solutions of the Cauchy-Jensen and the Additive-Quadratic Functional Equation in Paranormed Spaces [PDF]
International Journal of Analysis and Applications, 2019 In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the bi-Cauchy-Jensen functional equation and the bi-additive-quadratic functional equation in paranormed spaces.
Prondanai Kaskasem, Chakkrid Klin-eam
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Stability of a Bi-Jensen Functional Equation II
Journal of Inequalities and Applications, 2009 We investigate the stability of the bi-Jensen functional equation II f((x+y)/2,z)−f(x,z)−f(y,z)=0, 2f(x,(y+z)/2)−f(x,y)−f(x,z)=0 in the spirit of Găvruta.
Lee Yang-Hi, Jun Kil-Woung, Jung Il-Sook
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Stability of a Cauchy-Jensen Functional Equation in Quasi-Banach Spaces [PDF]
Journal of Inequalities and Applications, 2010 We obtain the generalized Hyers-Ulam stability of the Cauchy-Jensen functional equation .
Park Won-Gil, Bae Jae-Hyeong
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Iterator Operator Norm Estimation for Solutions to a Class of Elliptic Equations in Orlicz Space
Journal of Harbin University of Science and Technology, 2023 To study the related estimation of iterative operators on differential form, we apply the Jensen inequality, Young equation , G (p, q, C) class function and Whithey coverage theorem to extend the Lp estimation of A-harmonic equation of Green and Dirac ...
LÜ Yue ming, LI Xiao huan
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Ulam Stability of Jensen Functional Inequality on a Class of Noncommutative Groups
Journal of Function Spaces, 2023 In the paper, we introduce new ρ-functional inequalities related to the Jensen functional equation and some properties. The Hyers-Ulam stability of functional inequalities is proved.
Gang Lu +3 more
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Stability of Jensen functional equation on semigroups [PDF]
, 2010 In this paper we introduce a Jensen type functional equation on semigroups and study the Hyers–Ulam stability of this equation.
Faĭziev, Valeriĭ A., Riedel, Thomas
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Some hyperstability and stability results for the Cauchy and Jensen equations
Journal of Inequalities and Applications, 2022 In this paper we give some hyperstability and stability results for the Cauchy and Jensen functional equations on restricted domains. We provide a simple and short proof for Brzdȩk’s result concerning a hyperstability result for the Cauchy equation.
Mohammad Bagher Moghimi, Abbas Najati
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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 \
Park, Chun-Gil, Park, Won-Gil
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