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Note that T is continuous in view of continuity of f, (I_{k}), and g.
Note that (mathcal{A}) is continuous in view of continuity of f, (I_{k}), and (overline{I}_{k}).
Proof It is obvious that G is continuous in view of continuity of f, I k and I k ∗.
Proof It is easy to see that the operator A λ : P → P is continuous in view of continuity of G and f.
The operator (T: C[0,1]to C[0,1]) is continuous in view of continuity of (G t,s)) and (g t,u(t))).
The operator (S_{lambda}:mathscr{P}rightarrow mathscr{P}) is continuous in view of continuity of (G t,s)), (a(t)) and (f(x t))).
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Suppose that (f t,y,D_{q}y)) is continuous on ([0,1]times[0,+infty timesmathbb{R}). Then the mapping (T: Pto P) is completely continuous. In view of the expression of (G t,qs)), it is clear that (Tyin C[0,1]cap C^{1}[0,1], Ty(t geqslant0), and (Ty(t)) is continuous.
The study of the dynamics taking place during power system blackouts is a subject that receives continuous attention in view of its inherent complexity and relevant consequences.
It is known that the performance of continuous distillation in view of the energy conservation can significantly be improved by adopting the alternate-flow periodic operation which was first proposed and investigated by Cannon and his coworkers.
He developed the research conception, provided continuous support in view of data analysis, interpretation of results, reviewed and contributed to the manuscript writing and revisions.
Use continuous exposure to BPA in view of the ubiquitous and continuous exposure to BPA in humans.
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