Characterizations for vectorial prequasi-invex type functions via Jensen type inequalities (Q2790757)

Let \(K\) be a convex set in \(\mathbb R^n\) and \(F : K \longrightarrow \mathbb R\) a given numerical function. We say that \(f\) satisfies Jensen's inequality if NEWLINE\[NEWLINE f(\alpha x + (1 - \alpha) y) \leq \alpha f(x) + (1 - \alpha) f(y) \;\;\forall x, y \in K,\, \alpha \in (0,1). NEWLINE\]NEWLINE Jensen's inequality and its modifications were used in the literature to formulate some necessary and sufficient conditions which the function \(f\) must satisfy to have certain global properties as e.g. continuity, semicontinuity, prequasi-convexity or prequasi-invexity. The author proposes to use Jensen-type inequalities to derive criteria for vectorial prequasi-invex, semistrictly prequasi-invex and strictly prequasi-invex functions.