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Now suppose that the derivative of the considered function is bounded from below and above.
To obtain the main result, we assume that the absolute value of the derivative of the considered function is convex.
Some of these principles take advantage of equipping the considered function spaces with topologies of uniform convergence on compact subintervals.
Since even the simplest one-dimensional scalar conservation laws like the Burgers' equation have classical solutions only in some special cases, one has to broaden the considered function space of possible solutions.
So in this section instead of the convexity of derivative we consider the boundedness of the derivative and a Lipschitzian condition for the derivative of the considered function respectively to obtain new estimation type results.
In what follows, we replace this assumption with the boundedness of the derivative and with a Lipschitzian condition for the derivative of the considered function to obtain new estimation type results.
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Considered functions include: the floor, ceiling, truncation, and rounding-off functions.
The greatest values of the considered functions are infinite, when k 0 = ∞.
Unlike a furniture designer or jeweler, an artist, making a painting, is free to work without considering function.
Consider function f first.
So do you look at the pieces you make primarily as art, and by the way, they have a function, or do you consider function primarily?
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