19.3.13 Linear Operators

Condition: Prove that the operator \ (a x (t) = \ lambda \ int_ {0}^{t} x (s) d s+1 \) for \ (| \ lambda | <1 \) is compressing B \ (C [0.1] \). Find the motionless point of this operator at \ (\ lambda = 0.5 \). Make three iterations by the method of sequential approaches \ (\ left (x_ {0} (t) = 0 \ right) \). Find the relative and absolute errors of the found close solutions.