in hilbert space l2(rn), we prove the equivalence between the mod-ulus of smoothness and the k-functionals constructed by the sobolev space cor-responding to the fourier transform. for this purpose, using a spherical meanoperator.

We study the convergence rates of solutions to drift-diiusion systems (arising from plasma, semiconductors and electrolytes theories) to their self-similar or steady states. This analysis involves entropy-type Lyapunov functionals and logarithmic Sobolev inequalities.

We study the convergence rates of solutions to drift-diiusion systems (arising from plasma, semiconductors and electrolytes theories) to their self-similar or steady states. This analysis involves entropy-type Lyapunov functionals and logarithmic Sobolev inequalities.

In this paper we investigate maximum principles for functionals defined on solutions to special partial differential equations of elliptic type, extending results by Payne and Philippin. We apply such maximum principles to investigate one overdetermined problem.

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game’s expected payoff fu...

This paper is a companion to work of Feferman, Jäger, Glaß, and Strahm on the proof theory of the type two functionals μ and E1 in the context of Feferman-style applicative theories. In contrast to the previous work, we analyze these two functionals in the context of Schlüter’s weakened applicative basis PRON which allows for an interpretation in the primitive recursive indices. The proof-theor...

| In a recent paper certain approximations to continuous nonlinear functionals deened on an Lp space (1 < p < 1) are shown to exist. These approximations may be realized by sigmoidal neural networks employing a linear input layer that implements nite sums of integrals of a certain type. In another recent paper similar approximation results are obtained using elements of a general class of conti...

This paper is devoted to the analysis of a bilinear optimal control problem subject to the Fokker-Planck equation. The control function depends on time and space and acts as a coefficient of the advection term. For this reason, suitable integrability properties of the control function are required to ensure well-posedness of the state equation. Under these low regularity assumptions and for a g...

We consider positive linear operators having the same fundamental functions and different functionals in front of them. For differences involving such operators, we obtain Voronovskaja-type quantitative results. Applications illustrating theoretical aspects are presented.

The ordinary type of information data for approximation of functions f or functionals of them in the univariate case consists of function values {f(x1), . . . , f(xm)}. The classical Lagrange interpolation formula and the Gauss quadrature formula are famous examples. The simplicity of the approximation rules, their universality, the elegancy of the proofs and the beauty of these classical resul...