中文摘要：

本文考虑了Farkas引理,Gordan引理及其拓展形式之间的关系,从理论上证明了其等价性并说明了Farkas引理在各种等价形式中的重要地位,并指出了Gordan引理实际是可看作是Farkas引理的弱形式,然后研究了Farkas引理及其它形式在锥线性不等式组中的推广.

英文摘要：

This paper discusses the relationships among Farkas lemma,Gordan lemma, Motzkin theorem and Kuhn-Fourier theorem.The equivalences of Farkas lemma,Motzkin theorem and Kuhn-Fourier theorem are proved,and Gordan lemma can be considered as a corollary of Farkas lemma.Then we discussed the applications of Farkas lemma in analyzing the solvability of systems of inequalities.Finally,some generalizations of Farkas lemma for the systems of generalized inequalities are considered.