11). Unfortunately, this is usually not the case. 26) where B is a selfadjoint linear operator on a real Hilbert space H. 27) where P 1 is the orthogonal projection on some subspace H 1, P 2 = I - P 1 is the orthogonal projection on the orthogonal complement H 2 of H l' b1 = II B II, and B2 is a selfadjoint operator defined in H 2 such that IIB211 = b2 < b 1• Successive approximations Xn = BX n- 1 to the trivial solution of the equation x = Bx are defined by (n = 1,2, ... ). Let IIP1xoil > 0. 29) where y(p} is a continuous nonnegative function, monotone decreasing for p-+ +0, such that y(O} = O.
Approximate Solution of Operator Equations by M.A. Krasnosel'skii, G.M. Vainikko, R.P. Zabreyko, Ya.B. Ruticki, V.Va. Stet'senko