Then and are closed linear subspaces of.
where and,, are closed linear operators; is a Banach space; the history,, belongs to some abstract phase space defined axiomatically are appropriated functions.
(1.2). where, are closed linear operators defined on a common domain which is dense in a Banach space, and represent the Caputo derivative of defined by (1.3).
Let (A D(A)subseteq Erightarrow E), (B D(B subseteq Erightarrow E) be closed linear operators defined on a Banach space E satisfying (D(A cap D(B neq{0}).
where A t) : X → X are closed linear operators on a Banach space (X, || ⋅ ||), f, I i, and t i satisfy suitable conditions that will be established later and the symbol Δξ (t) represents the jump of the function ξ at t, which is defined by Δξ (t) = ξ (t+) − ξ(t−).
The operators A : D ( A ) ⊂ X → Y and E : D ( E ) ⊂ X → Y satisfy the following hypotheses: ( H 1 ) A and E are closed linear operators, ( H 2 ) D ( E ) ⊂ D ( A ) and E is bijective, ( H 3 ) E − 1 : Y → D ( E ) is continuous.
Throughout this paper, is a Banach space, and,, are closed linear operators defined on a common domain which is dense in ; the notations and represent the resolvent set of the operator and the domain of endowed with the graph norm, respectively.
When the chamber is closed, linear temperature and water vapour pressure gradients are established.
The linear relationship between the biomass and the difference in average soil salinity between poplar and control stands was close to linear (Fig. 6).
It was reported that the emptying curve of liquid food was in accord with single exponential model [23], but curve of solid food digested easily was close to linear type [24].
