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A class of \(G\)-semipreinvex functions and optimality. (English) Zbl 1271.90059

Summary: A class of \(G\)-semipreinvex functions, which are some generalizations of the semipreinvex functions, and the \(G\)-convex functions, is introduced. Examples are given to show their relations among \(G\)-semipreinvex functions, semipreinvex functions and \(G\)-convex functions. Some characterizations of \(G\)-semipreinvex functions are also obtained, and some optimality results are given for a class of \(G\)-semipreinvex functions. Our results improve and generalize some known results.

MSC:

90C25 Convex programming
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