The authors consider the two-point boundary problem for a linear differential equation with linearly transformed argument. The iteration algorithm of monoparametric aggregation-iterational method is constructed and its convergence is proved.

[1] Krasnoselskyi M.A., Lifshits E.A., Sobolev A.V. Positive linear systems. M: Nauka, 1985. - 255 p.

[2] Kurpel N.S. Projection-iterative methods of solving operator equations. - K.: Naukova dumka, 1968. 243 p.

[3] Shuvar B.A. On iterative aggregation and the method of successive approximations // Visnyk Lviv. Polytechnic Institute. - Lviv. 1991. P. 139-141.

[4] Shuvar B.A., Mentynskyi 2.M. Two-way algorithm for approximating solutions of the boundary value problem of Vallée Poussin // Mat. Methods and Phys.-Mechanical Fields. 2004.- Vol. 47, № 3. P. 33-36.

[5] Shuvar B.A., Kostyshyn L.P. Application of a single aggregation-iterative method to boundary value problems//Mat. Methods and Phys. Mechanical Fields. 2002. - Vol. 45, № 2. P. 31-36.

[6] KatoT., McLeod J.V. Thefunctional differential equation $y' = ay(x) + by (λx)$ //Bull.AmericanMath.Ѕос.-1971.-77.Р.891-937.

[7] Kuk K., Rossovsky L.E., Skubachevskii + A.L. A boundary value problem for a functional differential equation with a linearly transformed argument // Difference, equations. 1995. - 31, № 7. - P . 1366-370.

[8] Ronto A.N., Samoilenko A.M. On the unique solvability of some boundary-value problems for functional differential equations in Banach space // Add. NAS of Ukraine. - 2002. - № 9. - P. 42-46.

[9] Grebenshchikov B.G., Lozhnikov A.V. Stabilization of a system containing a constant and linear delay // Differ. equations - 2004. - 40, N 12. - P.1587-1595.