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Zbl 1094.26008
On generalized preinvex functions and monotonicities.
(English)
[J] JIPAM, J. Inequal. Pure Appl. Math. 5, No. 4, Paper No. 110, 9 p., electronic only (2004). ISSN 1443-5756/e

The generalization of preinvexity considered in this paper consists in replacing $\eta (x^{1},x^{2})$ by $\alpha (x^{1},x^{2})\eta (x^{1},x^{2})$ in the definition of invexity [see {\it S. R. Mohan} and {\it S. K. Neogy}, J. Math. Anal. Appl. 189, No. 3, 901--908 (1995; Zbl 0831.90097)], $\alpha$ being a given bifunction. The functions satisfying the resulting condition are said to be $\alpha$-preinvex with respect to $\eta$. Obviously, a function is $\alpha$-preinvex with respect to $\eta$ if and only if it is preinvex with respect to $\alpha \eta$. All results in the paper follow from this simple observation.
[Juan-Enrique Mart\'inez-Legaz (Barcelona)]
MSC 2000:
*26B25 Convexity and generalizations (several real variables)
26A48 Monotonic functions, generalizations (one real variable)

Keywords: preinvex functions; generalized monotonicity

Citations: Zbl 0831.90097

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