Some Ionescu-Weitzenbck' s type inequalities for general triangles are presented. The main tool in the proofs is Radon's inequality and of course Ionescu-Weitzenbck s inequality.DUMITRU M. B?TINE?UGIURGIUNECULAI STANCIUBibliotheca Publishing HouseJournal of Science & Arts...
By the triangle inequality we have \begin{aligned} u(y)-u(x)=d_\lambda (z,y)-d_\lambda (z,x)\le d_\lambda (x,y) \end{aligned} Recall that, when X=\{\frac{\partial }{\partial x_j}\}_{1\le j\le n} or when X is given by Carnot type Hörmander vector fields, one...
Barza, S., Kolyada, V., Soria, J.: Sharp constants related to the triangle inequality in Lorentz spaces. Trans. Am. Math. Soc. 361(10), 5555–5574 (2009) Article MathSciNet Google Scholar Bennett, C., Sharpley, R.: Interpolation of operators. Pure and Applied Mathematics, 129, Aca...
Outline Abstract Keywords 1. Introduction 2. The proofs of our results 3. Final remarks on colouring for (H1,H2)-free graphs 4. The clique-width of (sP1,Kt−e)-free graphs ReferencesShow full outline Cited by (28) Figures (3)Theoretical...
Note that equality is attained in the previously discussed example with half of the equal to and the other half equal to , thanks to the binomial theorem. To prove this identity, we consider the polynomial Evaluating this polynomial at , taking absolute values, using the triangle inequality,...
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The procedure entails first making an educated guess at a suitable axis map, then printing instances throughout the optical size range—each at the appropriate point size, and evaluating the proofs to determine if the axis map needs to be adjusted further to achieve better results. NOTE: Refer...
$$ over a triangle $$t_{\delta}:= \bigl\{ (\xi,\eta):0 < \xi< \xi_{0}-2 \delta, \xi+ \delta< \eta< \xi_{0} - \delta \bigr\} $$ and then over the rectangle $$\pi_{\delta}:= \bigl\{ (\xi,\eta): 0 < \xi< \xi_{0}-2 \delta, \xi_{0} + \delta<...
Using the triangle inequality shows the first bound.To show the second one, we add and subtract and use Proposition 3.6 (consistency) and the contractivity of \pi _{h} to obtainThe bound on this term follows by Proposition 3.8 (approximation property) and proceeding analogously for the term ...