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 Annales Universitatis Mariae Curie-Sklodowska, sectio A – MathematicaNumber of Followers: 1     Open Access journal ISSN (Print) 0365-1029 - ISSN (Online) 2083-7402 Published by Wydawnictwo UMCS  [25 journals]
• On a new two-parameter generalization of dual-hyperbolic Jacobsthal
numbers

• Authors: Dorota Bród, Anetta Szynal-Liana, Iwona Włoch
Pages: 1 - 14
Abstract: In this paper we introduce two-parameter generalization of dualhyperbolic Jacobsthal numbers: dual-hyperbolic (s,p)-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, d’Ocagne identities. Moreover, we give the generating function, matrix generator and summation formula for these numbers.
PubDate: 2021-07-24
DOI: 10.17951/a.2021.75.1.1-14
Issue No: Vol. 75, No. 1 (2021)

• Weighted integral inequalities related to Wirtinger’s result for
p-norms with applications

• Authors: Silvestru Sever Dragomir
Pages: 15 - 36
Abstract: In this paper we establish several natural consequences of some Wirtinger type integral inequalities for p-norms. The corresponding weighted versions and applications related to the weighted trapezoid inequalities, to weighted Gruss’ type inequalities and reverses of Jensen’s inequality are also provided.
PubDate: 2021-07-24
DOI: 10.17951/a.2021.75.1.15-36
Issue No: Vol. 75, No. 1 (2021)

• Exponential representations of injective continuous mappings in radial
sets

• Authors: Magdalena Jastrzębska, Dariusz Partyka
Pages: 37 - 51
Abstract: By a radial set we understand a non-empty set $$A \subset \mathbb{C} \setminus \{0\}$$ such that for every point $$z\in A$$ the circle with centre at the origin and passing through $$z$$ is included in $$A$$. We show in a detailed manner that every continuous and injective function $$F : A \to \mathbb{C} \setminus \{0\}$$ can be represented by means of the natural exponential function $$\text{exp}$$ and a certain continuous function $$\varPhi : \text{Ei}(A) \to \mathbb{C}$$, where $$\text{Ei}(A)$$ is the set of all $$z \in \mathbb{C}$$ with the property $$\text{exp}(iz) \in A$$. The representation is given by $$F(\text{exp}(iz)) = \text{exp}(i\varPhi (z))$$ for $$z \in \text{Ei}(A)$$. We also touch the problem of the injectivity of $$\varPhi$$.
PubDate: 2021-07-24
DOI: 10.17951/a.2021.75.1.37-51
Issue No: Vol. 75, No. 1 (2021)

• Regular matrix methods of summability and real interpolation

• Authors: Andrzej Kryczka, Konrad Kurlej
Pages: 53 - 59
Abstract: We show that the Banach–Saks property with respect to a regular positive matrix method of summability is inherited by the real interpolation spaces from a space forming the interpolation family and possessing this property. The proof refers to the Galvin–Prikry theorem on Ramsey sets. The results apply to several matrix methods of summability, such as Cesaro, Nørlund or Holder methods.
PubDate: 2021-07-24
DOI: 10.17951/a.2021.75.1.53-59
Issue No: Vol. 75, No. 1 (2021)

• On lifting of 2-vector fields to $$r$$-jet prolongation of the tangent
bundle

• Authors: Jan Kurek, Włodzimierz Mikulski
Pages: 61 - 67
Abstract: If $$m \geq 3$$ and $$r \geq 1$$, we prove that any natural linear operator $$A$$ lifting 2-vector fields $$\Lambda \in \Gamma (\bigwedge^2 TM)$$ (i.e., skew-symmetric tensor fields of type (2,0)) on $$m$$-dimensional manifolds $$M$$ into 2-vector fields $$A(\Lambda)$$ on $$r$$-jet prolongation $$J^rTM$$ of the tangent bundle $$TM$$ of $$M$$ is the zero one.
PubDate: 2021-07-24
DOI: 10.17951/a.2021.75.1.61-67
Issue No: Vol. 75, No. 1 (2021)

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