Acta et Commentationes Universitatis Tartuensis de Mathematica

Narayana numbers as sums of two base b repdigits

Prasanta Kumar Ray, Kisan Bhoi, Bijan Kumar Patel — Tue, 22 Nov 2022 15:52:49 +0200

In this study, we find all Narayana numbers which are expressible as sums of two base b repdigits. The proof of the main result uses lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker–Davenport reduction method.

Properties of theta-H-compact sets in hereditary m-spaces

Ahmad Al-Omari, Takashi Noiri — Tue, 22 Nov 2022 00:00:00 +0200

Let (X,m, H) be a hereditary m-space. A subset A of X is said to be θ-H-compact relative to X if for every cover U of A by m(θ)-open sets of X, there exists a finite subset U₀ of U such that A \ ∪ U₀ ∈ H. We obtain several properties of these sets. Also, we define and investigate two kinds of strong forms of “θ-H-compact relative to X”.

On Pellnomial coefficients and Pell-Catalan numbers

Ahmet İpek — Tue, 22 Nov 2022 17:03:38 +0200

In this paper, we first give the Pascal’s identity for Pellnomial coefficients and then we show that the Pellnomial coefficients are integers. We obtain that the product of r consecutive Pell numbers is divisible by the Pell analog of r!. Also, we introduce the divisibility theorems between Pell numbers and Pellnomial coefficients. Furthermore, we first define Pell–Catalan numbers and then we derive two formulas for presenting Pell–Catalan numbers.

On some properties of CV_{(0)}(X, A)

Lourdes Palacios, Pavel Ramos-Martinez, Carlos Signoret — Wed, 23 Nov 2022 13:37:47 +0200

Let X be a completely regular Hausdorff space and V a Nachbin family on X. For a locally convex algebra A, let CV₍₀₎(X, A) be the algebra of all weighted vector-valued continuous functions with the topology given by the uniform seminorms induced by V . In this paper we study some properties of A that are inherited by CV₍₀₎(X, A). These properties are related to the unit element, spectral seminorms and uniformly A-convex property.

Rate of convergence for rational and conjugate rational Fourier series of functions of generalized bounded variation

Hardeepbhai Khachar, Rajendra Vyas — Wed, 23 Nov 2022 14:48:28 +0200

In this article, extending the results of Fourier and conjugate Fourier series, the rates of convergence for rational and conjugate rational Fourier series for functions of generalized bounded variation are estimated.

Unique common fixed points through a unified condition

Hakima Bouhadjera — Wed, 23 Nov 2022 00:00:00 +0200

Fixed point theory is a crucial branch in mathematics with a colossal number of applications in countless subjects. It furnishes preeminent tools and resources for elucidating varied problems which at first glance do not look like a fixed point problem. Since and even before 1912 till now several authors launched the existence and uniqueness of common fixed points for pairs of single and set-valued maps satisfying certain compatibilities on different spaces. This paper proves existence and uniqueness of a common fixed point for pairs of occasionally weakly biased maps. This unique common fixed point is guaranteed under the concept of modified contractive modulus function. Our theorems improve some results existing in the fixed point literature.

Applications of degenerate q-Euler and q-Changhee polynomials with weight α

Ömer Duran, Neşe Ömür, Sibel Koparal — Mon, 28 Nov 2022 10:36:13 +0200

In this paper, we give new identities involving degenerate q-Euler polynomials with weight α and q-Changhee polynomials of the second kind with weight α, using the Faà di Bruno formula and some identities of the Bell polynomials of the second kind.

Tensor product of partial acts

Heleen Saarse, Kristo Väljako — Mon, 28 Nov 2022 11:00:08 +0200

In this article we define the tensor product of partial acts over a semigroup and prove several properties of this tensor product. We also define the notion of a polite partial biact, which is needed to define partial actions on the tensor product of partial acts. Finally, we prove that a certain tensor functor of partial acts is left adjoint of a certain hom-functor of partial acts.

On a generalized class of analytic functions related to Bazilevič functions

Laxmipriya Parida, Teodor Bulboaca, Ashok Kumar Sahoo — Mon, 28 Nov 2022 11:50:28 +0200

Using operator L_p(a, c) introduced by Saitoh (Math. Japon. 44 (1996), 31–38) we define the subclass H_p,n^ν,μ (a, c; ϕ) of the class A(p, n) and establish containment, subordination and coefficient inequalities of this subclass. We indicate the connections of our results with earlier results obtained by other researchers.

Asymmetric response of inelastic circular plates to blast loading

Annely Mürk, Jaan Lellep — Mon, 28 Nov 2022 12:04:37 +0200

The dynamic behaviour of clamped circular plates subjected to the concentrated blast loading is studied. The load is applied at a non-central point of the plate, non-axisymmetric deflections are taken into account. An approximate theoretical procedure developed earlier is applied for the evaluation of residual maximal deflections. The solution technique is based on the idea of equality of the power of the internal and external work, respectively. As it was shown earlier this concept leads to results which are close to exact ones in the case of axisymmetric loading of circular plates, also in the case of circular cylindrical shells.