General convex sets and convex functions : g - convex sets and g - convcx functions are investigated , some properties of which arc achieved , the cti - tcrions of g - convcx functions and g - quasiconvcx functions arc given , the theory of general convexity is deepen : two kinds of general variational inequality problems are studied 討論了一類廣義的凸集和凸函數(shù): g -凸集和g -凸函數(shù),得出了若干性質(zhì),給出了g -凸函數(shù)和g -擬凸函數(shù)的判別準則,豐富了廣義凸性的內(nèi)容;研究了兩類廣義的變分不等式問題。