Linear conjugate boundary value problems

Linear conjugate boundary value problems are studied in this paper. We obtain a kind of contractive mapping by means of meromorphic approximation. Using this map we discuss solvability conditions and the number of solutions for these problems. When solutions exist, we give their representations. In addition, several well-known important conclusions on Markushevich's problems, such as Noether's theorem in the steady case etc., can also be obtained as an immediate consequence of our results.