19.8.4 Integral Equations

Condition: Determine, under what \ (\ alpha \) display \ (a \) type \ (\ quad (a x) (t) (t) = \ alpha \ int_ {a}^{b} k (t, s) x (s) d s (t) \) is compressing in the space \ (c [a, b] \) \) \) \) \) \) \) \) \) \) \) \) \) \) Uniform norm, find its motionless point for sure, as well as approximately (having made four iterations). \ [\ begin {array} {l} k (t, s) = 2 t^{2} s+3 s, \ quad g (t) = 2 t^{2} -3 \\ a = 0, \ quad b = 1. \ end {Array} \]