Justifying the convergence of the rectangular method for complete singular integral equations with continuous coefficients on the circle

For an integral equation on the unit circle Gamma of the form (aI + bS + K)f = g, where a and b are Holder functions, S is a singular integration operator, and K is an integral operator with Holder kernel, we consider a method of solution based on the discretization of integral operators using the rectangle rule. This method is justified under the assumption that the equation is solvable in L-2(Gamma) and the coefficients a and b satisfy the strong ellipticity condition.