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On the other hand, if (Ggamma_{1}(x_{0})=Ggamma_{2}(x_{0})), then the convexity of (Ggamma_{1}) and (Ggamma_{2}) implies that (D_hat {alpha}(x_{0}) < D^hat{alpha}(x_{0})). So, problem (20) with conditions (V c)=gamma_{2c}), (V(d)=gamma_{2d}) has a solution in ([hat{alpha},beta]), but this contradicts the fact that (Ggamma_{2}) is the greatest solution for this problem in ([alpha,beta]).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com