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On generalized preinvex functions and monotonicities. (English) Zbl 1094.26008
The generalization of preinvexity considered in this paper consists in replacing η(x 1 ,x 2 ) by α(x 1 ,x 2 )η(x 1 ,x 2 ) in the definition of invexity [see S. R. Mohan and S. K. Neogy, J. Math. Anal. Appl. 189, No. 3, 901–908 (1995; Zbl 0831.90097)], α being a given bifunction. The functions satisfying the resulting condition are said to be α-preinvex with respect to η. Obviously, a function is α-preinvex with respect to η if and only if it is preinvex with respect to αη. All results in the paper follow from this simple observation.

MSC:
26B25Convexity and generalizations (several real variables)
26A48Monotonic functions, generalizations (one real variable)