Sentence examples for be checked that condition from inspiring English sources
By a careful calculation (there are 21 nontrivial cases) it can be checked that condition (3.2) (i.e., condition (3.3)) is satisfied for all X, S ∈ X 2. Hence, Theorem 2 can be applied to conclude that f has a coupled fixed point (which is ( 0, 0,) ).
It can be checked that the corresponding forcing term, initial condition, and boundary condition are respectively begin{aligned} &f x,t)=frac{2sin(pi x)}{Gamma 2-alpha)}t^{1-alpha}+frac {2sin (pi x)}{Gamma 2-alpha)}t^{1-alpha}+frac} sin(pi x)+pi ^{2sin{2}sin (pi x).
} end{aligned}It can be checked that for this equation the necessary condition holds for this equation.
It is easy to check that conditions (i), (ii), (iii) are satisfied.
However, it is easy to check that conditions (i) and (ii) in Corollary 2.3 are satisfied.
It is easy to check that conditions (i), (iii) in Theorem 3.1 hold.
It is not difficult to check that conditions (1.1) and (1.2) are consequences of the standard Calderón-Zygmund operator.
It is not difficult to check that conditions (B1 - B6) hold.
For sufficiently large t ∈ T, it is not difficult to check that conditions (B2 - B6), (2.2), and (3.17) hold.
we can check that conditions (8) are satisfied in both cases.
