2013, Studia Mathematica 12
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Simultaneous primality of the integers $n$ and $2n - d$
(2013)A necessary and sufficient condition for the simultaneous primality of integers $n$ and $2n-d$ is given by means of congruences ${mod n(2n - d)}$ that hold if and only if they form a prime pair. These are used to obtain ... -
On a sum form functional equation containing three unknown mappings
(2013)The general solutions of a sum form functional equation containing three unknown mappings have been obtained without imposing any regularity condition on any of three mappings. -
On Levinson's inequality
(2013)We give a very simple proof of the classical Levinson inequality and generalize the result by Mercer. -
The Littlewood-Paley g-function associated with the Riemann-Liouville operator
(2013)First, we study the Gauss and Poisson semigroups connected with the Riemann-Liouville operator. Next, we define and study the Littlewood- Paley $g$-function associated with the Riemann-Liouville operator for which we ... -
Approximation by some combinations of the Poisson integrals for Hermite and Laguerre expansions
(2013)The aim of this paper is the study of a rate of convergence of some combinations of the Poisson integrals for Hermite and Laguerre expansions. We are able to achieve faster convergence for our modified operators over ... -
Construction of an $A$-manifold on a principal torus bundle
(2013)We construct a new example of an $A$-manifold, i.e. a Riemannian manifold with cyclic-parallel Ricci tensor. This condition can be viewed as a generalization of the Einstein condition. The underlying manifold for ... -
Annales Universitatis Paedagogicae Cracoviensis. 128. Studia Mathematica 12
(Wydawnictwo Naukowe Uniwersytetu Pedagogicznego, Kraków, 2013)
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