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- W2950882577 abstract "In this paper, we point out a very flexible scheme within which a strict minimax inequality occurs. We then show the fruitfulness of this approach presenting a series of various consequences. Here is one of them: Let $Y$ be a finite-dimensional real Hilbert space, $J:Yto {bf R}$ a $C^1$ function with locally Lipschitzian derivative, and $varphi:Yto [0,+infty[$ a $C^1$ convex function with locally Lipschitzian derivative at 0 and $varphi^{-1}(0)={0}$. Then, for each $x_0in Y$ for wich $J'(x_0)neq 0$, there exists $delta>0$ such that, for each $rin ]0,delta[$, the restriction of $J$ to $B(x_0,r)$ has a unique global minimum $u_r$ which satisfies $$J(u_r)leq J(x)-varphi(x-u_r)$$ for all $xin B(x_0,r)$, where $B(x_0,r)={xin Y: |x-x_0|leq r} .$" @default.
- W2950882577 created "2019-06-27" @default.
- W2950882577 creator A5066441613 @default.
- W2950882577 date "2012-01-07" @default.
- W2950882577 modified "2023-09-27" @default.
- W2950882577 title "A strict minimax inequality criterion and some of its consequences" @default.
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