Acta Universitatis Sapientiae, Mathematica Feed

Two applications of Grunsky coefficients in the theory of univalent functions

Tue, 26 Dec 2023 00:00:00 GMT

Let S denote the class of functions f which are analytic and univalent in the unit disk 𝔻 = {z : |z| < 1} and normalized with f(z)=z+∑n=2∞αnzn {\rm{f}}\left( {\rm{z}} \right) = {\rm{z}} + \sum\nolimits_{{\rm{n = 2}}}^\infty {{\alpha _{\rm{n}}}{{\rm{z}}^{\rm{n}}}} . Using a method based on Grusky coefficients we study two problems over the class S: estimate of the fourth logarithmic coefficient and upper bound of the coefficient difference |α5| − |α4|.

Oscillatory behavior of second-order nonlinear noncanonical neutral differential equations

Tue, 26 Dec 2023 00:00:00 GMT

This paper discusses the oscillatory behavior of solutions to a class of second-order nonlinear noncanonical neutral differential equations. Sufficient conditions for all solutions to be oscillatory are given. Examples are provided to illustrate all the main results obtained.

Uniqueness of Dirichlet series in the light of shared set and values

Tue, 26 Dec 2023 00:00:00 GMT

In this article, we have studied the uniqueness problem of Dirichlet series, which is convergent in a right half-plane and having analytic continuation in the complex plane as a meromorphic function sharing some sets and values. Our first result partially improve a result of [Ann. Univ. Sci. Budapest., Sect. Comput., 48(2018), 117-128] by relaxing the sharing conditions. Most importantly, we have pointed out a number of big gaps in a recent paper [J. Contemp. Math. Anal., 56(2021), 80-86], which makes the existence of the paper under question. Finally, under a different approach, we have provided the corrected form of the result of [J. Contemp. Math. Anal., 56(2021), 80-86] as much as practicable.

Fixed point in ℳvb M_{\rm{v}}^{\rm{b}} – metric space and applications

Tue, 26 Dec 2023 00:00:00 GMT

The aim is to utilize a new metric called an Mvb M_{\rm{v}}^{\rm{b}} –metric which is an improvement and generalization of Mv−metric to revisit the celebrated Banach and Sehgal contractions in Mvb M_{\rm{v}}^{\rm{b}} –metric space. We demonstrate that the collection of open balls forms a basis on Mvb M_{\rm{v}}^{\rm{b}} -metric space. Further, we give some examples for the verification of established results. Towards the end, we solve a non-linear matrix equation and an equation of rotation of a hanging cable to substantiate the utility of these extensions.

Automorphisms of Zappa-Szép product fixing a subgroup

Tue, 26 Dec 2023 00:00:00 GMT

In this paper, we have found the automorphism group of the Zappa-Szép product of two groups fixing a subgroup. We have computed these automorphisms for a subgroup of order p2 of a group G which is the Zappa-Szép product of two cyclic groups in which one is of order p2 and other is of order m.

On relation-theoretic F−contractions and applications in F−metric spaces

Tue, 26 Dec 2023 00:00:00 GMT

The aim is to introduce some relation theoretic variants of F−contraction in an F−metric space endowed with a binary relation R and to prove results for its fixed point. In the sequel, several classes of contractions are sharpened, generalized, and improved. Numerical examples are presented to illustrate the theoretical conclusions. As applications of the main results, we solve a Dirichlet-Neumann initial value problem and two Dirichlet boundary value problems.

Norm and almost everywhere convergence of matrix transform means of Walsh-Fourier series

Tue, 26 Dec 2023 00:00:00 GMT

We show the uniformly boundedness of the L1 norm of general matrix transform kernel functions with respect to the Walsh-Paley system. Special such matrix means are the well-known Cesàro, Riesz, Bohner-Riesz means. Under some conditions, we verify that the kernels KnT=∑k=1ntk,nDk {\rm{K}}_{\rm{n}}^{\rm{T}} = \sum\nolimits_{{\rm{k = 1}}}^{\rm{n}} {{{\rm{t}}_{{\rm{k}},{\rm{n}}}}{{\rm{D}}_{\rm{k}}}} , (where Dk is the kth Dirichlet kernel) satisfy ‖KnT‖1≤c. {\left\| {{\rm{K}}_{\rm{n}}^{\rm{T}}} \right\|_1} \le {\rm{c}}{\rm{.}} As a result of this we prove that for any 1 ≤ p < ∞ and f ∈ Lp the Lp-norm convergence ∑k=1ntk,nSk(f)→f \sum\nolimits_{{\rm{k = 1}}}^{\rm{n}} {{{\rm{t}}_{{\rm{k}},{\rm{n}}}}{{\rm{S}}_{\rm{k}}}\left( {\rm{f}} \right)} \to {\rm{f}} holds. Besides, for each integrable function f we have that these means converge to f almost everywhere.

A survey of the maximal and the minimal nullity in terms of omega invariant on graphs

Tue, 26 Dec 2023 00:00:00 GMT

Let G = (V, E) be a simple graph with n vertices and m edges. ν(G) and c(G) = m − n + θ be the matching number and cyclomatic number of G, where θ is the number of connected components of G, respectively. Wang and Wong in [18] provided formulae for the upper and the lower bounds of the nullity η(G) of G as η(G) = n − 2ν(G) + 2c(G) and η(G) = n − 2ν(G) − c(G), respectively. In this paper, we restate the upper and the lower bounds of nullity η(G) of G utilizing omega invariant and inherently vertex degrees of G. Also, in the case of the maximal and the minimal nullity conditions are satisfied for G, we present both two main inequalities and many inequalities in terms of Omega invariant, analogously cyclomatic number, number of connected components and vertex degrees of G.

On k-semi-centralizing maps of generalized matrix algebras

Tue, 26 Dec 2023 00:00:00 GMT

Let 𝒢 = 𝒢 (A, M, N, B) be a generalized matrix algebra over a commutative ring with unity. In the present article, we study k-semi-centralizing maps of generalized matrix algebras.

A note on convolution of Janowski type functions with q-derivative

Wed, 15 Nov 2023 00:00:00 GMT

The purpose of the present paper is to introduce and study new subclasses of analytic functions which generalize the classes of Janowski functions with q-derivative. We also study certain a convolution conditions, and apply the convolution conditions to get sufficient condition and the neighborhood results related to the functions in the class 𝒮q(A, B, α).

Pre-Schur convex functions and some integral inequalities on domains from plane

Wed, 15 Nov 2023 00:00:00 GMT

In this paper we introduce the concept of pre-Schur convex functions defined on general domains from plane. Then, by making use of Green’s identity for double integrals, we establish some integral inequalities for this class of functions that naturally generalize the case of Schur convex functions. Some exmples for rectangles and disks are also provided.

On a new p(x)-Kirchhoff type problems with p(x)-Laplacian-like operators and Neumann boundary conditions

Wed, 15 Nov 2023 00:00:00 GMT

In this paper we study a Neumann boundary value problem of a new p(x)-Kirchhoff type problems driven by p(x)-Laplacian-like operators. Using the theory of variable exponent Sobolev spaces and the method of the topological degree for a class of demicontinuous operators of generalized (S+) type,weprove theexistenceofaweak solutionsof this problem. Our results are a natural generalisation of some existing ones in the context of p(x)-Kirchhoff type problems.

New family of bi-univalent functions with respect to symmetric conjugate points associated with Borel distribution

Wed, 15 Nov 2023 00:00:00 GMT

In this paper, we introduce and investigate a new family, denoted by 𝒲Σsc (λ, η, δ, r), of normalized holomorphic and bi-univalent functions with respect to symmetric conjugate points, defined in 𝕌, by making use the Borel distribution series, which is associated with the Horadam polynomials. We derive estimates on the initial Taylor-Maclaurin coefficients and solve the Fekete-Szeg˝o type inequalities for functions in this family.

Some new results on the prime order Cayley graph of given groups

Wed, 15 Nov 2023 00:00:00 GMT

In this paper, we study the prime order Cayley graph assigned to the group ℤn for different values of n. We specify some of the graph theoretical properties such as chromatic and perfect matching numbers. Furthermore, we determine the adjacency matrices and eigenvalues of the prime order Cayley graph associated with groups ℤn and 𝒟2n.

On the strong approximation of the non-overlapping k-spacings process with application to the moment convergence rates

Wed, 15 Nov 2023 00:00:00 GMT

In the present work, we establish the strong approximations of the empirical k-spacings process {αn(x): 0 ≤ x< ∞} (cf. (3)). We state the moment convergence rates results for this process.

On Menelaus’ and Ceva’s theorems in Nil geometry

Wed, 15 Nov 2023 00:00:00 GMT

In this paper we deal with Nil geometry, which is one of the homogeneous Thurston 3-geometries. We define the “surface of a geodesic triangle” using generalized Apollonius surfaces. Moreover, we show that the “lines” on the surface of a geodesic triangle can be defined by the famous Menelaus’ condition and prove that Ceva’s theorem for geodesic trianglesistruein Nil space. In our work we will use the projective model of Nil geometry described by E. Molnár in [6].

Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay

Wed, 15 Nov 2023 00:00:00 GMT

In this paper, singularly perturbed differential equations having both small and large delay are considered. The considered problem contains large delay parameter on the reaction term and small delay parameter on the convection term. The solution of the problem exhibits interior layer due to the delay parameter and strong right boundary layer due to the small perturbation parameter ε. The resulting singularly perturbed problem is solved using exponential fitted operator method. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, one model problem is considered for numerical experimentation.

Subclass of analytic functions with negative coefficients related with Miller-Ross-type Poisson distribution series

Wed, 15 Nov 2023 00:00:00 GMT

The purpose of the present paper is to find a necessary and sufficient condition for Miller-Ross-type Poisson distribution series to be in the class 𝒲δ(α, γ, β) of analytic functions with negative coefficients .Also, we investigate several inclusion properties of the classes 𝒮∗, 𝒦 and ℝτ(A, B) associated of the operator 𝕀ν,cm defined by this distribution. Further, we consider an integral operator related to Miller-Ross-type Poisson distribution series. Several corollaries and consequences of the main results are also considered.

Proofs, generalizations and analogs of Menon’s identity: a survey

Wed, 15 Nov 2023 00:00:00 GMT

Menon’s identity states that for every positive integer n one has ∑ (a − 1, n) = φ (n)τ(n), where a runs through a reduced residue system (mod n), (a − 1, n) stands for the greatest common divisor of a − 1 and n, φ(n) is Euler’s totient function, and τ(n) is the number of divisors of n. Menon’s identity has been the subject of many research papers, also in the last years. We present detailed, self contained proofs of this identity by using different methods, and point out those that we could not identify in the literature. We survey the generalizations and analogs, and overview the results and proofs given by Menon in his original paper. Some historical remarks and an updated list of references are included as well.

Partial sums of the Rabotnov function

Thu, 19 Jan 2023 00:00:00 GMT

This article deals with the ratio of normalized Rabotnov function ℝα,β (z) and its sequence of partial sums (ℝα,β)m (z). Several examples which illustrate the validity of our results are also given.