A system of partial differential equations with fractional derivatives.
A theorem about Carathéodory's superposition
A theorem of Galambos-Bojanić-Seneta type.
A theorem of Šarkovskii characterizing continuous maps of zero topological entropy
A theorem of the alternative and a two-function minimax theorem.
A theorem of the Hahn-Banach type and its applications
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.
A theory of linear differential equations with fractional derivatives
A theory of non-absolutely convergent integrals in Rn with singularities on a regular boundary
Specializing a recently developed axiomatic theory of non-absolutely convergent integrals in , we are led to an integration process over quite general sets 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.
A topology on inequalities.
A trilinear restriction problem for the paraboloid in .
A two-sided estimate of .
A two-weight inequality for the Bessel potential operator
Necessary conditions and sufficient conditions are derived in order that Bessel potential operator is bounded from the weighted Lebesgue spaces into when .
A typical property of the symmetric differential quotient
A Unified Approach to Methods for the Simultaneous Computation of All Zeros of Generalized Polynomials.
A unified approach to several inequalities involving functions and derivatives
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 -dimensional results are also given.
A Unified Theory of Regularly Varying Sequences.
A unified treatment of some sharp inequalities.
A variance analog of majorization and some associated inequalities.