Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


convexity

On the solvability of a class of nonlinear Hammerstein integral equations on the semiaxis

The paper studies a class of nonlinear integral equations on the semiaxis with a non-compact Hammerstein operator. It is assumed that the kernel of the equation decreases exponentially on the positive part of the number axis. Equations of this kind arise in various fields of natural science. In particular, such equations are found in the theory of radiation transfer in spectral lines, in the mathematical theory of the space-time propagation of an epidemic, in the kinetic theory of gases.

Convexity of Bounded Chebyshev Sets in Finite-dimensional Asymmetrically Normed Spaces

The well-known Tsar’kov’s characterisation of finite-dimensional Banach spaces in which every bounded Chebyshev set (bounded P-acyclic set) is convex is extended to the asymmetrical setting.