强G-半预不变凸函数的新性质探讨

Discussion for the New Properties of Strongly G-semi-preinvexity

本文讨论了强G-半预不变凸函数,它是强预不变凸函数与强G-预不变凸函数的真推广.首先,举例说明了强G-半预不变凸函数的存在性;然后,借助集合稠密性原理,获得了强G-半预不变凸函数的一个充要条件;最后,得到强G-半预不变凸函数在一定假设(在闭半连通集上)下的下确界就是函数在此集合上的最小值,所得结果推广并改进了相应文献中的结果.

The strongly G-semi-preinvex function is discussed in this paper, which is a true generalization of strongly semi-preinvex functions and strongly G-preinvex functions. Firstly, an example is given to illustrate the existence of strongly G-semipreinvex functions. Then, with the principle of set dense, a sufficiency and necessity of strongly G-semi-preinvex functions is obtained. Finally, the infimum of strongly G-semi-preinvex functions on a set is its minimum under some suitable conditions(in closed semi-connected set) is given. The obtained results generalize and improve the results in the corresponding literature.