An application of the generalized Maligranda–Orlicz's Lemma.
An approximate analog of a theorem of Khintchine
An approximation theorem for sequences of linear strains and its applications
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in by the sequence of linear strains of mapping bounded in Sobolev space . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.
An approximation theorem for sequences of linear strains and its applications
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in L1 by the sequence of linear strains of mapping bounded in Sobolev space W1,p . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.
An approximative generalization of Zahorski's theorem on derivative
An asymptotic form of Cauchy's functional equation.
An asymptotic form of Cauchy's functional equation. (Short Communication).
An axiomatic theory of non-absolutely convergent integrals in Rn
We introduce an axiomatic approach to the theory of non-absolutely convergent integrals. The definition of our ν-integral will be descriptive and depends mainly on characteristic null conditions. By specializing our concepts we will later obtain concrete theories of integration with natural properties and very general versions of the divergence theorem.
An effective method for solving fractional integro-differential equations.
An Egoroff-type theorem for set-valued measurable functions.
An elementary approach to some applications of nonstandard analysis
An elementary inequality.
An elementary proof of the convergence of iterated exponentials.
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