Following the formulations as in [6, 20 22], we generalize the classical stability problems of above functional equations to the spaces of generalized functions as.
This paper provides a risk analysis model that includes the capabilities of the above functional elements in order to guide the risk management, which includes attention to the effect of realistic error, e.g. of risk classification and risk damage assessment.
By using the above functional equations, we have the following theorem.
From the above functional equation, we get ∑ n = 0 ∞ ( x − u ) n t n n !
By using the above functional equation, we arrive at the following theorem.
Gilányi [15] and Fechner [16] proved the Hyers-Ulam stability of the above functional inequality.
and proved the Hyers-Ulam stability of the above functional equation in classical Banach spaces.
end{aligned} Unfortunately, the above functional I may be not well defined in (H^{1}(mathbb {R}^{3})).
We have proved the Hyers-Ulam stability of Jordan homomorphisms in Jordan-Banach algebras for the above functional equation.
Since M is continuous and f has subcritical growth, the above functional is of class C1 in H.
Using data-driven respiratory gating, we also demonstrated the effect of respiratory motion correction on estimating the above functional parameters from list mode patient data.
