A quasi-convex function is a real-valued function 
defined on a convex
subset 
for which, for all real 
, the set 
is convex.
This is equivalent to saying that 
is quasi-convex iff its negative 
is quasi-concave.
Quasi-Convex Function
See also
Convex, Convex Function, Pseudoconcave Function, Pseudoconvex Function, Quasi-Concave FunctionThis entry contributed by Christopher Stover
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References
Borwein, J. and Lewis, A. Convex Analysis and Nonlinear Optimization: Theory and Examples. New York: Springer Science+Business Media, 2006.Referenced on Wolfram|Alpha
Quasi-Convex FunctionCite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Quasi-Convex Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Quasi-ConvexFunction.html