The proof follows by applying Theorem 13 and using the facts that (f^{sigma}(t)=f(t)) and (h_{2} t, s)=frac{ t-s)^{2}}{2}) (from the first item of Definition 11 for the case (k=frac{ t-s
From the conditions of our theorem it is obvious that item (i) of Definition 1.1 is satisfied.
By the same reason ( u, q, η ) belongs to the function spaces given in item (1) of Definition 6.1.
(1.31) Then the operator P defined by equality (1.13) continuously acts from (A_{gamma_{0}}) to the space (L_{n}(]a, b])), and there exists the function (deltain D_{n}(]a, b])) such that item (i) of Definition 1.1 holds.
From inequality (1.17) of item (ii) of Definition 1.1, it follows that for any (x in A_{gamma_{0}}) boundary problem (2.49), (2.25) has the unique solution y in the space (widetilde{C}^{n-1, m}(]a, b])) such that (yinwidetilde {C}^{m-1}_{1}(]a, b])).
From (3.13) and the last inequality it is obvious that the operator P defined by equality (1.13) continuously acts from (A_{gamma_{0}}) to the space (L_{n}(]a, b])), and item (ii) of Definition 1.1 holds with (delta t, rho)=(1+kappa_{0} tum_{j=1}^{m}delta_{j}(t, rho)).
The main idea is that upon reaching this stage the term μ i, j was already computed, and thus β i, j can be computed efficiently, as implied by item 2 of Definition 1.
30 31 The OPTION Scale is composed of 12 items of operational definitions of different patient-involving skills, rated on a Likert scale from 0 (behaviour absent) to 4 (behaviour observed at an excellent skill level).
Firstly, we generated a questionnaire with candidate items for definitions of remission and relapse of PMR as retrieved in a literature search.
Items (i) and (ii) of Definition 2 hold true.
