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Zbl 1139.26006
Long, X.J.; Peng, J.W.
Semi-B-preinvex functions. (English)
[J] J. Optim. Theory Appl. 131, No. 2, 301-305 (2006). ISSN 0022-3239; ISSN 1573-2878/e

Summary: In this note, a class of functions, called semi-B-preinvex function, which are a generalization of the semipreinvex functions [{\it X.\,Q.\thinspace Yang} and {\it G.--Y.\thinspace 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 2000:: *26B25 Convexity and generalizations (several real variables)
90C26 Nonconvex programming

Keywords: semi-B-preinvex functions; B-vex functions; semi-invex sets; semipreinvex functions

Citations: Zbl 0779.90067; Zbl 0793.90069

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