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Semi-B-preinvex functions. (English) Zbl 1139.26006
Summary: In this note, a class of functions, called semi-B-preinvex function, which are a generalization of the semipreinvex functions [X. Q. Yang and G.–Y. Chen, J. Math. Anal. Appl. 169, No. 2, 359–373 (1992; Zbl 0779.90067)] and the B-vex functions [J. Optim. Theory Appl. 71, No. 2, 237–253 (1991; Zbl 0793.90069)], is introduced. Examples are given to show that there exist functions which are semi-B-preinvex functions, but are neither semipreinvex nor B-vex. A property of the semi-B-preinvex functions is obtained.
MSC:
26B25Convexity and generalizations (several real variables)
90C26Nonconvex programming, global optimization
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