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 of the form (aI + bS + K)f = g, where a and b are Hölder functions, S is a singular integration operator, and K is an integral operator with Hölder 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 L₂() and the coefficients a and b satisfy the strong ellipticity condition.