Lagrange multiplier rules for extremals in linear spaces

The aim of this paper is to formulate extremals in real, linear spaces, and to derive necessary conditions in the form of Lagrange multiplier rules for the extremals. Using a separation of intrinsic cores in real, linear spaces, the multiplier rules are proved under some conditions.The author wishes to thank the referee for a number of valuable suggestions, particularly the proof of Theorem 3.1.