Real functions as traces of Infinte polynomials.
Refinements of Carleman's inequality.
Refinements of results about weighted mixed symmetric means and related Cauchy means.
Refinements of the Hermite-Hadamard inequality for convex functions.
Régularité Gevrey au sens de Beurling ou Roumieu pour l'opérateur ... dans des ouverts non bornés.
Regularization of closed-valued multifunctions in a non-metric setting
Remarks of germs in infinite dimensions.
Remarks on the Bourgain-Brezis-Mironescu Approach to Sobolev Spaces
For a function the notion of p-mean variation of order 1, is defined. It generalizes the concept of F. Riesz variation of functions on the real line ℝ¹ to ℝⁿ, n > 1. The characterisation of the Sobolev space in terms of is directly related to the characterisation of by Lipschitz type pointwise inequalities of Bojarski, Hajłasz and Strzelecki and to the Bourgain-Brezis-Mironescu approach.
Remarks on the comparison of weighted quasi-arithmetic means
We present comparison theorems for the weighted quasi-arithmetic means and for weighted Bajraktarević means without supposing in advance that the weights are the same.
Remarks on the spaces of differentiable multifunctions
In this paper we consider some spaces of differentiable multifunctions, in particular the generalized Orlicz-Sobolev spaces of multifunctions, we study completeness of them, and give some theorems.
Residue class rings of real-analytic and entire functions
Let 𝓐(ℝ) and 𝓔(ℝ) denote respectively the ring of analytic and real entire functions in one variable. It is shown that if 𝔪 is a maximal ideal of 𝓐(ℝ), then 𝓐(ℝ)/𝔪 is isomorphic either to the reals or a real closed field that is an η₁-set, while if 𝔪 is a maximal ideal of 𝓔(ℝ), then 𝓔(ℝ)/𝔪 is isomorphic to one of the latter two fields or to the field of complex numbers. Moreover, we study the residue class rings of prime ideals of these rings and their Krull dimensions. Use is made of...
Riemann type integrals for functions taking values in a locally convex space
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
Schur geometric convexity for differences of means.
Schur-convexity of averages of convex functions.
Schur-convexity of two types of one-parameter mean values in variables.
Selection theorem in L¹
Let F be a multifunction from a metric space X into L¹, and B a subset of X. We give sufficient conditions for the existence of a measurable selector of F which is continuous at every point of B. Among other assumptions, we require the decomposability of F(x) for x ∈ B.
Seminorm generating relations and their Minkowski functionals.
Separation by monotonic functions.
Separation via quadratic functions.
Separation via quadratic functions. (Summary).