Galerkin method operator differential equations with Lipschitz continuous coefficients
General nonlinear random equations with random multivalued operator in Banach spaces.
General regularizing functionals for solving ill-posed problems in Lebesgue spaces.
General system of -monotone nonlinear variational inclusions problems with applications.
General viscosity approximation methods for common fixed points of nonexpansive semigroups in Hilbert spaces.
General ways of constructing accelerating Newton-like iterations on partially ordered topological spaces.
Generalized Mann iterations for approximating fixed points of a family of hemicontractions.
Generalized set-valued variational-like inclusions and Wiener--Hopf equations in Banach spaces.
Generic convergence of iterates for a class of nonlinear mappings.
Geometric characteristics for convergence and asymptotics of successive approximations of equations with smooth operators
We discuss the problem of characterizing the possible asymptotic behaviour of the iterates of a sufficiently smooth nonlinear operator acting in a Banach space in small neighbourhoods of a fixed point. It turns out that under natural conditions, for the most part of initial approximations these iterates tend to "lie down" along a finite-dimensional subspace generated by the leading (peripherical) eigensubspaces of the Fréchet derivative at the fixed point and moreover the asymptotic behaviour of...