#### For citation:

Salimov R. B. To a Solution of the Inhomogeneous Riemann–Hilbert Boundary Value Problem for Analytic Function in Multiconnected Circular Domain in a Special Case. *Izvestiya of Saratov University. Mathematics. Mechanics. Informatics*, 2013, vol. 13, iss. 3, pp. 52-58. DOI: 10.18500/1816-9791-2013-13-3-52-58

# To a Solution of the Inhomogeneous Riemann–Hilbert Boundary Value Problem for Analytic Function in Multiconnected Circular Domain in a Special Case

The author offers a new approach to solution of the Riemann–Hilbert boundary value problem for analytic function in multiconnected circular domain. This approach is based on construction of solution of corresponding homogeneous problem, when analytic in domain function is being defined by known boundary values of its argument. The author considers a special case of a problem when the index of a problem is more than zero and on unit of less order of connectivity of domain. Resolvability of a problem depends on number of solutions of some system of the linear algebraic equations.

- Salimov R. B. Modification of new approach to solution of the Hilbert boundary value problem for analytic function in multi-connected circular domain. Izv. Saratov. Univ. N.S. Ser. Math. Mech. Inform., 2012, vol. 12, iss. 1, pp. 32–38 (in Russian)
- .Vekua I. N. Generalized analytic functions. Oxford, Pergamon Press, 1962, 668 p. (Rus. ed.: Vekua I. N. Obobshchennye analiticheskie funktsii. Moscow, Fizmatgiz, 1959, 628 p.)
- Gahov F. D. Boundary-Value Problems. Moscow, Nauka, 1977, 640 p. (in Russian).
- Muskhelishvili N. I. Singular Integral Equations. Boundary-Value Problems of the Theory of Functions and Some of Their Applications to Mathematical Physics. Moscow, Nauka, 1968, 511 p. (in Russian).
- Salimov R. B. Some properties of analytic in a disc functions and their applications to study of behaviour of singular integrals. Russian Math. (Izvestiya VUZ. Matematika), 2012, vol. 56, no. 3, pp. 36–44.

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