One problem of D. S. Mitrinovič and its generalization
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Kragujevac Journal of Mathematics
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Nikola Rosić (2001)
Kragujevac Journal of Mathematics
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Abdon Atangana, Dumitru Baleanu, Ahmed Alsaedi (2015)
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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.
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An elementary short proof of the one-dimensional Rademacher theorem on differentiability of Lipschitz functions is given.
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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 . 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...