Recent results concerning the existence and uniqueness of mild and classical solutions for non-local Cauchy problems are extended to the following non-autonomous semilinear integrodifferential equation u′(t) = A(t) [ u(t) + ∫ t 0 F (t, s)u(s) ds ] + f(t, u(t)), 0 ≤ t ≤ T, u(0) + g(t1, . . . , tp, u(t1), . . . , u(tp)) = u0, in a Banach space X, with A(·) the generators of strongly continuous se...

In this paper, we provide a complete study of the spectrum constant coefficients differential operator on scale localized Sobolev spaces, $$H^{s}_{\mathrm{loc}}(I),$$ which are Fréchet spaces. This is quite different from what find in literature, where all relevant results concerned with Banach Our aim to understand behavior three types (point, residual, and continuous) relation between them th...

Let E be a real Banach space, let C be a closed convex subset of E, let T be a nonexpansive mapping of C into itself, that is, ‖Tx−Ty‖ ≤ ‖x− y‖ for each x, y ∈ C, and let A⊂ E×E be an accretive operator. For r > 0, we denote by Jr the resolvent of A, that is, Jr = (I + rA)−1. The problem of finding a solution u∈ E such that 0∈ Au has been investigated by many authors; for example, see [3, 4, 7,...

We study the spectrum of multipliers (bounded operators commuting with the shift operator S) on a Banach space E of sequences on Z. Given a multiplier M , we prove that f M(σ(S)) ⊂ σ(M) where f M is the symbol of M . We obtain a similar result for the spectrum of an operator commuting with the shift on a Banach space of sequences on Z. We generalize the results for multipliers on Banach spaces ...

Let E be a Banach space over C and let the densely defined closed linear operator A: D(A) ... EQ E be discretely approximated by the sequence ((An, D(An)))n ¥N of operators An where each An is densely defined in the Banach space Fn. Let sa(A) be the approximate point spectrum of A and let se(An) denote the e-pseudospectrum of An. Generalizing our own result, we show that sa(A) ... lim inf se(An...

This article concernes the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search a solution in an infinite dimensional Banach space having only a finite number of data available. In this sense the situation is applicalble to a large variety of applications where a measurement process delivers a discretization of an i...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...