An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions.
An elementary proof of the one-dimensional Rademacher theorem
An elementary short proof of the one-dimensional Rademacher theorem on differentiability of Lipschitz functions is given.
An elementary proof of the preservation of Lipschitz constants by the Meyer-König and Zeller operators.
An elementary proof of the theorem that absolute gauge integrability implies Lebesgue integrability
It is commonly known that absolute gauge integrability, or Henstock-Kurzweil (H-K) integrability implies Lebesgue integrability. In this article, we are going to present another proof of that fact which utilizes the basic definitions and properties of the Lebesgue and H-K integrals.
An Elementary Treatise on the Integral Calculus [Book]
An embedding theorem for Sobolev type functions with gradients in a Lorentz space
The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.
An equation in the left and right fractional derivatives of the same order
An Equation With Left and Right Fractional Derivatives
An equivalent form of the fundamental triangle inequality and its applications.
An estimate in the spirit of Poincaré's inequality
An even easier proof of monotonicity of Stolarsky means
An example concerning small changes of commuting functions
An example of a function, which is not a d.c. function
Let , . We construct a function which has Lipschitz Fréchet derivative on but is not a d.c. function.
An example of a -smooth function whose gradient range is an arc with no tangent at any point.
An example of a continuous function without the usual, the approximative and the distributional derivative
An example of a function which is locally constant in an open dense set, everywhere differentiable but not constant
An example of a genuinely discontinuous generically chaotic transformation of the interval
It is proved that a piecewise monotone transformation of the unit interval (with a countable number of pieces) is generically chaotic. The Gauss map arising in connection with the continued fraction expansions of the reals is an example of such a transformation.
An example of infinitely many sinks for smooth interval maps.
An Expansion Formula for Fractional Derivatives and its Application
An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is derived. The convergence of the series is proved and an estimate of the reminder is given. The form of the fractional derivative given here is especially suitable in deriving restrictions, in a form of internal variable theory, following from the second law of thermodynamics, when applied to linear viscoelasticity of fractional derivative type.
An extended Hardy-Hilbert inequality and its applications.