A Note on Lipschitz Classes.
A note on logarithmically completely monotonic ratios of certain mean values.
A note on Lusin's condition (N)
A note on martingale transforms and -weights
A note on Mathieu's inequality.
A note on Mathieu's inequality.
A note on metric preserving functions.
A note on mixed-mean inequalities.
A note on multivalued Baire category theorem
A note on Newton's inequality.
A note on Ostrowski like inequalities.
A note on Ostrowski like inequalities in spaces.
A note on Ostrowski's inequality.
A note on partial derivatives of convex functions
A note on propagation of singularities of semiconcave functions of two variables
P. Albano and P. Cannarsa proved in 1999 that, under some applicable conditions, singularities of semiconcave functions in propagate along Lipschitz arcs. Further regularity properties of these arcs were proved by P. Cannarsa and Y. Yu in 2009. We prove that, for , these arcs are very regular: they can be found in the form (in a suitable Cartesian coordinate system) , , where , are convex and Lipschitz on . In other words: singularities propagate along arcs with finite turn.
A note on quasiconvex functions that are pseudoconvex.
In the present note we consider the definitions and properties of locally pseudo- and quasiconvex functions and give a sufficient condition for a locally quasiconvex function at a point x ∈ Rn, to be also locally pseudoconvex at the same point.
A note on separate continuity and connectivity properties
Separately continuous functions are shown to have certain properties related to connectedness.
A note on separation of sets by approximately continuous functions
A note on signs of Kloosterman sums
We prove that the sign of Kloosterman sums changes infinitely often as runs through the square-free numbers with at most prime factors. This improves on a previous result by Sivak-Fischler who obtained 18 instead of 15. Our improvement comes from introducing an elementary inequality which gives lower and upper bounds for the dot product of two sequences whose individual distributions are known.
A note on some expansions of p-adic functions
Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by . The system is defined in the space C(ℤₚ,ℂₚ) of ℂₚ-valued continuous functions on ℤₚ. J. Rutkowski has also considered some questions concerning expansions of functions from C(ℤₚ,ℂₚ) with respect to . This paper is a remark to Rutkowski’s paper. We define another system in C(ℤₚ,ℂₚ), investigate its properties and compare it to the system defined by Rutkowski. The system...