An alternative Jensen's functional equation on semigroups [PDF]
ScienceAsia, 2012 We study the alternative Jensen's functional equation f(x) 2f(xy) + f(xy 2 ) = 0 when f is a ...
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Stability of Jensen functional equation on semigroups
Journal of Mathematical Analysis and Applications, 2010 A real function \(f\) defined on a semigroup \(S\) is Jensen if it satisfies the functional equation \(f(xyz)+f(xzy)+2f(x)-2f(xy)-2f(xz)=0\). In this paper, the authors investigate the Hyers-Ulam stability of the above equation and prove that each semigroup can be embedded into a semigroup such that the equation above is stable.
Faĭziev, Valeriĭ A., Riedel, Thomas
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On a Sum Form Functional Equation Related to Various Nonadditive Entropies in Information Theory
, 2016 [[abstract]]In this paper, the general solutions of a sum form functional equation containing four unknown mappings have been obtained without imposing any regularity condition on any of the four mappings.
Dhiraj Kumar Singh, Prem Nath
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GENERALIZED JENSEN'S FUNCTIONAL EQUATIONS AND APPROXIMATE ALGEBRA HOMOMORPHISMS
Bulletin of the Korean Mathematical Society, 2002 The generalized Hyers-Ulam-Rassias stability of the functional equation \[ 2^nf\biggl({{x_1+\dots+x_{2^n}}\over{2^n}}\biggr)=\sum_{i=1}^{2^n}f(x_i)\tag{1} \] is proved in Banach modules over a~unital \(C^{\ast}\)-algebra. The Hyers-Ulam-Rassias stability of algebra homomorphisms between Banach algebras associated with the functional equation (1) is ...
Bae, Jae-Hyeong, Park, Won-Gil
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The Jensen functional equation in non‐Archimedean normed spaces [PDF]
Journal of Function Spaces, 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. In particular, we show that a mapping f between non‐Archimedean spaces with f(0) = 0 is additive if and only if as max {‖x‖, ‖y‖} → ∞.
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A primer on Variational Laplace (VL). [PDF]
Neuroimage, 2023 Zeidman P, Friston K, Parr T.
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Diversity and its causes: Lewontin on racism, biological determinism and the adaptationist programme. [PDF]
Philos Trans R Soc Lond B Biol Sci, 2022 Shen H, Feldman MW.
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Estimations of f- and Rényi divergences by using a cyclic refinement of the Jensen's inequality
, 2019 The Jensen's inequality plays a crucial role to obtain inequalities for divergences between probability distributions. In this paper we introduce a new functional, based on the f-divergence functional, and then we obtain some estimates for the new ...
Horváth, László +2 more
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A New Criterion for Exponential Stability of a Class of Hopfield Neural Network with Time-Varying Delay Based on Gronwall's Inequality. [PDF]
Comput Intell Neurosci, 2021 Guo F, Luo R, Qin X, Yi Y.
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Phytoplankton competition and resilience under fluctuating temperature. [PDF]
Ecol Evol, 2023 Siegel P +3 more
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