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Results of Tadeusz Świa̧tkowski on algebraic sums of sets and their applications in the theory of subadditive functions
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Janusz Matkowski
Published/Copyright:
June 5, 2012
Abstract.
A refinement of Steinhaus' theorem on the algebraic sum of subsets of 
due to Raikov (1939) was not known to the mathematical community
and still is not popular. In 1994, Tadeusz Świa̧tkowski, being not aware
of the existence of Raikov's theorem, proved another result of this type.
Unfortunately, a few days later he passed away.
In this paper we present the theorems of Świa̧tkowski and Raikov and we
apply them in the theory of subadditive type inequalities. An improvement of
a converse of Minkowski's inequality theorem is presented.
Keywords: Algebraic sum of sets; density of set at a point; interior point; Steinhaus theorem; Raikov theorem; subadditive function
Received: 2010-06-28
Revised: 2011-01-28
Accepted: 2011-04-28
Published Online: 2012-06-05
Published in Print: 2012-06-01
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Algebraic sum of sets;
density of set at a point;
interior point;
Steinhaus theorem;
Raikov theorem;
subadditive function
Articles in the same Issue
- Masthead
- Regularity theory for superquadratic energy functionals related to nonlinear Hencky materials in three dimensions
- Common fixed points of nonexpansive mappings with applications to best and best simultaneous approximation
- Perturbations of the matrix logarithm
- Strong convergence theorems for relatively quasi-nonexpansive mappings, variational inequality problems and systems of generalized mixed equilibrium problems
- Results of Tadeusz Świa̧tkowski on algebraic sums of sets and their applications in the theory of subadditive functions
- The generalized Stokes theorem for ℝ-linear forms on Lie algebroids
- Certain classes of multivalent functions with negative coefficients involving the Hadamard product
- Projective coordinates and compactification in elliptic, parabolic and hyperbolic 2-D geometry
- Location of zeros of polynomials
