Which operator is not linear?
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Examples of non-linear operators. where K(t,s,u), a≤t, s≤b, −∞<u<∞, is a function such that g(t)=∫baK(t,s,x(s))ds is continuous on [a,b] for any x(s)∈C(a,b)( for example, K(t,s,u) is continuous on a≤t, s≤b, −∞<u<∞). If K(t,s,u) is non-linear in u, then A is a non-linear Urysohn operator mapping C[a,b] into itself.
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