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Let Y be a subgroup of an abelian group X and let T be a given collection of subsets of a linear space E over the rationals. Moreover, suppose that F is a subadditive set-valued function defined on X with values in T. We establish some conditions under which every additive selection of the restriction of F to Y can be extended to an additive selection of F. We also present some applications of results of this type to the stability of functional equations.

A theoretical development of distance measure for intuitionistic fuzzy numbers.

Guha, Debashree, Chakraborty, Debjani (2010)

International Journal of Mathematics and Mathematical Sciences

A theory of linear differential equations with fractional derivatives

T. M. Atanacković, S. Pilipović, B. Stanković (2012)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

A theory of non-absolutely convergent integrals in Rn with singularities on a regular boundary

W. Jurkat, D. Nonnenmacher (1994)

Fundamenta Mathematicae

Specializing a recently developed axiomatic theory of non-absolutely convergent integrals in $ℝ^{n}$ , we are led to an integration process over quite general sets $A \subseteq q ℝ^{n}$ with a regular boundary. The integral enjoys all the usual properties and yields the divergence theorem for vector-valued functions with singularities in a most general form.

A theory on perturbations of the Dirac operator.

Collier Melescue, Suzanne (1999)

Journal of Inequalities and Applications [electronic only]

A topology on inequalities.

D'Aristotile, Anna Maria, Fiorenza, Alberto (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

A trilinear restriction problem for the paraboloid in $ℝ^{3}$ .

Bennett, Jonathan (2004)

Electronic Research Announcements of the American Mathematical Society [electronic only]

A two-sided estimate of $e^{x} - {(1 + \frac{x}{n})}^{n}$ .

Niculescu, Constantin P., Vernescu, Andrei (2004)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

A two-weight inequality for the Bessel potential operator

Yves Rakotondratsimba (1997)

Commentationes Mathematicae Universitatis Carolinae

Necessary conditions and sufficient conditions are derived in order that Bessel potential operator $J_{s, λ}$ is bounded from the weighted Lebesgue spaces $L_{v}^{p} = L^{p} (ℝ^{n}, v (x) d x)$ into $L_{u}^{q}$ when $1 < p \leq q < \infty$ .

A typical property of the symmetric differential quotient

Jiří Matoušek (1989)

Colloquium Mathematicae

A Unified Approach to Methods for the Simultaneous Computation of All Zeros of Generalized Polynomials.

Andreas Frommer (1989)

Numerische Mathematik

A unified approach to several inequalities involving functions and derivatives

Javier Duoandikoetxea (2001)

Czechoslovak Mathematical Journal

There are many inequalities measuring the deviation of the average of a function over an interval from a linear combination of values of the function and some of its derivatives. A general setting is given from which the desired inequalities are obtained using Hölder’s inequality. Moreover, sharpness of the constants is usually easy to prove by studying the equality cases of Hölder’s inequality. Comparison of averages, extension to weighted integrals and $n$ -dimensional results are also given.

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