The aim of this study is the approximation of a solution x* of a ganeralized equation 0 in f(x)+F(x) in Banach spaces, where f is a single-valued function whose second order Frechet derivative satisfies an Hölder condition and F stands for a set-valed map with closed graph. Using a fixed point theorem and the Aubin property of F, we show the existe...

We prove a new sharp Kolmogorov-type inequality that estimates the uniform norm of a mixed derivative of fractional order (in the sense of Marchaud) of a function of several variables via the uniform norm of the function and its norm on Hölder spaces.

We construct Sobolev-Morrey type spaces with dominant mixed derivatives and, using the obtained integral representation, prove some embedding theorems in these spaces.

We consider a boundary value problem in the unit disk for an elliptic equation of order N with constant coefficients. We suppose, that the characteristic equation has exactly M pairs of complex conjugate roots (0 ≤ 2M ≤ N). The solution of this problem belongs to the class of N times continuously differentiable functions, which with up to the (N − ...

We show that every ‘conveniently Hölder’ homomorphism between Lie groups in the sense of convenient differential calculus is smooth (in the convenient sense). In particular, every ℓip0-homomorphism is smooth.