On two mean value properties and functional equations associated with them.
On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions
2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (of normalized analytic and univalent functions in the open unit disk U), and in its subclasses (as the classes S∗ of the starlike functions and K of the convex functions in U). Among these operators, two operators introduced...
On uniform approximation of bounded approximately continuous functions by differences of lower semicontinuous and approximately continuous ones
On uniform symmetric derivatives
On uniqueness of conjugacy of continuous and piecewise monotone functions.
On variation topology
On variations of functions of one real variable
We discuss variations of functions that provide conceptually similar descriptive definitions of the Lebesgue and Denjoy-Perron integrals.
On vector functions of bounded convexity
Let be a normed linear space. We investigate properties of vector functions of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity is equal to the variation of on . As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.
On Volterra inequalities and their applications.
On weak Hessian determinants
We consider and study several weak formulations of the Hessian determinant, arising by formal integration by parts. Our main concern are their continuity properties. We also compare them with the Hessian measure.
On weak type inequalities for rare maximal functions
The properties of rare maximal functions (i.e. Hardy-Littlewood maximal functions associated with sparse families of intervals) are investigated. A simple criterion allows one to decide if a given rare maximal function satisfies a converse weak type inequality. The summability properties of rare maximal functions are also considered.
On weakly Gibson -measurable mappings
A function f: X → Y between topological spaces is said to be a weakly Gibson function if for any open connected set U ⊆ X. We prove that if X is a locally connected hereditarily Baire space and Y is a T₁-space then an -measurable mapping f: X → Y is weakly Gibson if and only if for any connected set C ⊆ X with dense connected interior the image f(C) is connected. Moreover, we show that each weakly Gibson -measurable mapping f: ℝⁿ → Y, where Y is a T₁-space, has a connected graph.
On weighted dyadic Carleson's inequalities.
On weighted Hadamard-type singular integrals and their applications.
On weighted Hardy and Poincaré-type inequalities for differences.
On weighted Hardy inequalities on semiaxis for functions vanishing at the endpoints.
On weighted inequalities with geometric mean operator generated by the Hardy-type integral transform.
On weighted inequality of Hardy type for higher order derivatives
On weighted norm integral inequality of g. h. Hardy's type
On weighted Ostrowski type inequalities for operators and vector-valued functions.