Normal solvability and 𝜙-accretive mappings of Banach spaces

A New Method for Proving Existence Theorems for Abstract Hammerstein Equations

“…(ii) there exists > 0 such that, for each 1 , 2 ∈ ( ), We need the following definition which was given by Browder [17].…”

Свойства Выпуклости Образов Нелинейных Интегральных Операторов

“…Известные нам утверждения о свойствах выпуклости образов нелинейных операторов общего вида ограничи-ваются теоремой [1] о выпуклости замыкания F (X) для максимально монотон-ного по Минти-Браудеру оператора F : X → 2 X * в рефлексивном банаховом пространстве X. Для φ-аккретивных операторов F : X → Y в паре банаховых пространств (X, Y ) аналогичное утверждение см. в [2]. В то же время неиз-вестно сколько-нибудь широких классов интегральных операторов вида (1) со свойством (максимальной) монотонности или аккретивности.…”

Range of Gateaux differentiable operators and local expansions

“…Many authors (see [3], [4], [7], [10], [13], [16] and [17]) have studied domain invariance or surjectivity of accretive operators. The following theorem gives an improvement of Theorem 4.11 of [4], Corollary 2.2 of [6] and Theorem 3.4 of [13].…”

“…Let P be a nonlinear operator from a Banach space X into a Banach space 7. Many authors (see [3], [4], [6], [7], [10], [12], [13], [14] and [15]) have studied solvability of the equation Px = y, for y e Y, a considerable number of which involve local or infinitesimal assumptions on the operator P, by showing that P is surjective. However, in many cases, in general P need not be surjective, although for some y G y, the equation Px = y is solvable.…”