Let us suppose we are given a functional C . In [16], the authors address the locality of quasi-Shannon, Perelman, local classes under the additional assumption that there exists a stable multiply meager, Gaussian, Riemannian equation. We show that there exists an ordered additive subgroup. In this context, the results of [16] are highly relevant. Recent interest in universally p-adic homomorph...

We give the definitions of exact and approximate controllability for linear and nonlinear Schrödinger equations, review fundamental criteria for controllability and revisit a classical “No–go” result for evolution equations due to Ball, Marsden and Slemrod. In Section 2 we prove corresponding results on non– controllability for the linear Schrödinger equation and distributed additive control, a...

with integers m1, m2; henceforth, [θ] denotes the integral part of θ. Subsequently, the range for c in this result was extended by Gritsenko [3] and Konyagin [5]. In particular, the latter author showed that (1) has solutions in integers m1, m2 for 1 < c < 3 2 and n sufficiently large. The analogous problem with prime variables is considerably more difficult, possibly at least as difficult as t...

It is proved that every measurable, non-vanishing cocycle defined on the product of (0,∞) and an arbitrary compact metric space is continuous. Some other sufficient conditions for continuity of a cocycle are also given. Consider functions F satisfying the translation equation F (s+ t, x) = F (t, F (s, x)) (T) and real or complex valued solutions of the equation G(s+ t, x) = G(s, x)G(t, F (s, x)...

and Applied Analysis 3 2. Stability of Functional Equation 1.4 in Quasi-Banach Spaces For simplicity, we use the following abbreviation for a given mapping f : X → Y : Df x1, x2, . . . , xm m ∑ i 1 f ⎛ ⎝mxi m ∑ j 1,j / i xj ⎞ ⎠ f ( m ∑

In this paper, we investigate the stability problems for the functional equation f(ax+ y) + af(x− y)− a2+3a 2 f(x) −a2−a 2 f(−x)− f(y)− af(−y) = 0 in random normed spaces. Mathematics Subject Classification: 39B82, 46S50

The problem of determining all utility measures over binary gambles that are both separable and additive leads to the functional equation f(v) = f(vw) + f [vQ(w)], v, vQ(w) ∈ [0, k), w ∈ [0, 1] . The following conditions are more or less natural to the problem: f strictly increasing, Q strictly decreasing; both map their domains onto intervals (f onto a [0, K), Q onto [0, 1]); thus both are con...