Displaying similar documents to “An example of a continuous function without the usual, the approximative and the distributional derivative”

New properties of conformable derivative

Abdon Atangana, Dumitru Baleanu, Ahmed Alsaedi (2015)

Open Mathematics

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Recently, the conformable derivative and its properties have been introduced. In this work we have investigated in more detail some new properties of this derivative and we have proved some useful related theorems. Also, some new definitions have been introduced.

On generalized Peano and Peano derivatives

H. Fejzić (1993)

Fundamenta Mathematicae

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A function F is said to have a generalized Peano derivative at x if F is continuous in a neighborhood of x and if there exists a positive integer q such that a qth primitive of F in the neighborhood has the (q+n)th Peano derivative at x; in this case the latter is called the generalized nth Peano derivative of F at x and denoted by F [ n ] ( x ) . We show that generalized Peano derivatives belong to the class [Δ’]. Also we show that they are path derivatives with a nonporous system of paths satisfying...

Derivative of the Donsker delta functionals

Herry Pribawanto Suryawan (2019)

Mathematica Bohemica

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We prove that derivatives of any finite order of Donsker's delta functionals are well-defined elements in the space of Hida distributions. We also show the convergence to the derivative of Donsker's delta functionals of two different approximations. Finally, we present an existence result of finite product and infinite series of the derivative of the Donsker delta functionals.

Distributionally regulated functions

Jasson Vindas, Ricardo Estrada (2007)

Studia Mathematica

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We study the class of distributions in one variable that have distributional lateral limits at every point, but which have no Dirac delta functions or derivatives at any point, the "distributionally regulated functions." We also consider the related class where Dirac delta functions are allowed. We prove several results on the boundary behavior of functions of two variables F(x,y), x ∈ ℝ, y>0, with F(x,0⁺) = f(x) distributionally, both near points where the distributional point value...

Distributions that are functions

Ricardo Estrada (2010)

Banach Center Publications

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It is well-known that any locally Lebesgue integrable function generates a unique distribution, a so-called regular distribution. It is also well-known that many non-integrable functions can be regularized to give distributions, but in general not in a unique fashion. What is not so well-known is that to many distributions one can associate an ordinary function, the function that assigns the distributional point value of the distribution at each point where the value exists, and that...