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Hence (1.1) has extremal weak solutions in which, moreover, satisfy (5.6) and (5.5).
Theorem 5.3 implies that (1.1) has extremal weak solutions in which, moreover, satisfy (5.6) and (5.5) with replaced by.
Then, by application of Lemma 4.2, we obtain that G has the extremal fixed points in ([alpha,beta]), say (V^), (V_), which moreover satisfy (19).
If ({Tu_{n}} _{n in mathbb {N}}) converges whenever ({u_{n}}_{nin mathbb {N}}) is a monotone sequence in ([a,b]) then the operator T has the greatest, (u^), and the least, (u_), fixed point in ([a,b]), which, moreover, satisfy u^=max{u : u le Tu},qquad u_=min{u : Tu le u}.
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If there is a mapping (F : mathbf{R} to Y) satisfying the inequality biglVert f(x) - F x) bigrVert leqtheta| x |^{p} (18) for any (x inmathbf{R} backslash{ 0 }), and if F, moreover, satisfies (4) for all (x inmathbf{R}), then F is a unique mapping satisfying (4) and (18).
Kapsner (2012) refers to a logic that satisfies AT, AT′, BT, and BT′ and, moreover, satisfies the requirement that (a) in no model A→~A is satisfiable (for any A) and (b) in no model A→B and A→~B are simultaneoulsy satisfiable (for any A and B), as strongly connexive, whereas if the conditions (a) and (b) are not both satisfied, the system is only called weakly connexive.
Moreover satisfies (5.14).
Moreover, satisfies the integral equation.
Moreover, satisfies the conclusions in Lemma 2.7.
Moreover, satisfies the following relations on : (3.10).
Moreover, satisfies the Riccati difference equation (2.2) and for sufficiently large.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com