rss_2.0Acta Universitatis Sapientiae, Mathematica FeedSciendo RSS Feed for Acta Universitatis Sapientiae, Mathematica Universitatis Sapientiae, Mathematica Feed of Zappa-Szép product fixing a subgroup<abstract> <title style='display:none'>Abstract</title> <p>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 p<sup>2</sup> of a group G which is the Zappa-Szép product of two cyclic groups in which one is of order p<sup>2</sup> and other is of order m.</p> </abstract>ARTICLEtrue behavior of second-order nonlinear noncanonical neutral differential equations<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue of Dirichlet series in the light of shared set and values<abstract> <title style='display:none'>Abstract</title> <p>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., <bold>48</bold>(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., <bold>56</bold>(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., <bold>56</bold>(2021), 80-86] as much as practicable.</p> </abstract>ARTICLEtrue and almost everywhere convergence of matrix transform means of Walsh-Fourier series<abstract> <title style='display:none'>Abstract</title> <p>We show the uniformly boundedness of the L<sub>1</sub> 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 <inline-formula> <alternatives> <inline-graphic xmlns:xlink="" xlink:href="graphic/j_ausm-2023-0013_eq_001.png"/> <mml:math xmlns:mml="" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mtext>K</mml:mtext></mml:mrow><mml:mtext>n</mml:mtext><mml:mtext>T</mml:mtext></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mtext>k</mml:mtext><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mtext>n</mml:mtext></mml:msubsup><mml:mrow><mml:msub><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow><mml:mrow><mml:mtext>k</mml:mtext><mml:mo>,</mml:mo><mml:mtext>n</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>D</mml:mtext></mml:mrow><mml:mtext>k</mml:mtext></mml:msub></mml:mrow></mml:mrow></mml:math> <tex-math>{\rm{K}}_{\rm{n}}^{\rm{T}} = \sum\nolimits_{{\rm{k = 1}}}^{\rm{n}} {{{\rm{t}}_{{\rm{k}},{\rm{n}}}}{{\rm{D}}_{\rm{k}}}}</tex-math> </alternatives> </inline-formula>, (where D<sub>k</sub> is the kth Dirichlet kernel) satisfy <disp-formula> <alternatives> <graphic xmlns:xlink="" xlink:href="graphic/j_ausm-2023-0013_eq_002.png"/> <mml:math xmlns:mml="" display="block"><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mrow><mml:mo>‖</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mtext>K</mml:mtext></mml:mrow><mml:mtext>n</mml:mtext><mml:mtext>T</mml:mtext></mml:msubsup></mml:mrow><mml:mo>‖</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mo>≤</mml:mo><mml:mtext>c</mml:mtext><mml:mtext>.</mml:mtext></mml:mrow></mml:math> <tex-math>{\left\| {{\rm{K}}_{\rm{n}}^{\rm{T}}} \right\|_1} \le {\rm{c}}{\rm{.}}</tex-math> </alternatives> </disp-formula></p> <p>As a result of this we prove that for any 1 <italic>≤</italic> p &lt; ∞ and f ∈ L<sub>p</sub> the L<sub>p</sub>-norm convergence <inline-formula> <alternatives> <inline-graphic xmlns:xlink="" xlink:href="graphic/j_ausm-2023-0013_eq_003.png"/> <mml:math xmlns:mml="" display="inline"><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mtext>k</mml:mtext><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mtext>n</mml:mtext></mml:msubsup><mml:mrow><mml:msub><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow><mml:mrow><mml:mtext>k</mml:mtext><mml:mo>,</mml:mo><mml:mtext>n</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>S</mml:mtext></mml:mrow><mml:mtext>k</mml:mtext></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mtext>f</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>→</mml:mo><mml:mtext>f</mml:mtext></mml:mrow></mml:math> <tex-math>\sum\nolimits_{{\rm{k = 1}}}^{\rm{n}} {{{\rm{t}}_{{\rm{k}},{\rm{n}}}}{{\rm{S}}_{\rm{k}}}\left( {\rm{f}} \right)} \to {\rm{f}}</tex-math> </alternatives> </inline-formula> holds. Besides, for each integrable function f we have that these means converge to f almost everywhere.</p> </abstract>ARTICLEtrue applications of Grunsky coefficients in the theory of univalent functions<abstract> <title style='display:none'>Abstract</title> <p>Let <italic>S</italic> denote the class of functions f which are analytic and univalent in the unit disk 𝔻 = {z : |z| &lt; 1} and normalized with <inline-formula> <alternatives> <inline-graphic xmlns:xlink="" xlink:href="graphic/j_ausm-2023-0017_eq_001.png"/> <mml:math xmlns:mml="" display="inline"><mml:mrow><mml:mtext>f</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mtext>z</mml:mtext><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mtext>z</mml:mtext><mml:mo>+</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mtext>n</mml:mtext><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mo>∞</mml:mo></mml:msubsup><mml:mrow><mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mtext>n</mml:mtext></mml:msub><mml:msup><mml:mrow><mml:mtext>z</mml:mtext></mml:mrow><mml:mtext>n</mml:mtext></mml:msup></mml:mrow></mml:mrow></mml:math> <tex-math>{\rm{f}}\left( {\rm{z}} \right) = {\rm{z}} + \sum\nolimits_{{\rm{n = 2}}}^\infty {{\alpha _{\rm{n}}}{{\rm{z}}^{\rm{n}}}}</tex-math> </alternatives> </inline-formula>. Using a method based on Grusky coefficients we study two problems over the class <italic>S</italic>: estimate of the fourth logarithmic coefficient and upper bound of the coefficient difference |α<sub>5</sub>| − |α<sub>4</sub>|.</p> </abstract>ARTICLEtrue k-semi-centralizing maps of generalized matrix algebras<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue relation-theoretic F−contractions and applications in F−metric spaces<abstract> <title style='display:none'>Abstract</title> <p>The aim is to introduce some relation theoretic variants of F−contraction in an F−metric space endowed with a binary relation <italic>R</italic> 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.</p> </abstract>ARTICLEtrue survey of the maximal and the minimal nullity in terms of omega invariant on graphs<abstract> <title style='display:none'>Abstract</title> <p>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 [<xref ref-type="bibr" rid="j_ausm-2023-0019_ref_018">18</xref>] 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.</p> </abstract>ARTICLEtrue point in – metric space and applications<abstract> <title style='display:none'>Abstract</title> <p>The aim is to utilize a new metric called an <inline-formula> <alternatives> <inline-graphic xmlns:xlink="" xlink:href="graphic/j_ausm-2023-0015_eq_002.png"/> <mml:math xmlns:mml="" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mtext>v</mml:mtext><mml:mtext>b</mml:mtext></mml:msubsup></mml:mrow></mml:math> <tex-math>M_{\rm{v}}^{\rm{b}}</tex-math> </alternatives> </inline-formula>–metric which is an improvement and generalization of M<sub>v</sub>−metric to revisit the celebrated Banach and Sehgal contractions in <inline-formula> <alternatives> <inline-graphic xmlns:xlink="" xlink:href="graphic/j_ausm-2023-0015_eq_003.png"/> <mml:math xmlns:mml="" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mtext>v</mml:mtext><mml:mtext>b</mml:mtext></mml:msubsup></mml:mrow></mml:math> <tex-math>M_{\rm{v}}^{\rm{b}}</tex-math> </alternatives> </inline-formula>–metric space. We demonstrate that the collection of open balls forms a basis on <inline-formula> <alternatives> <inline-graphic xmlns:xlink="" xlink:href="graphic/j_ausm-2023-0015_eq_004.png"/> <mml:math xmlns:mml="" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mtext>v</mml:mtext><mml:mtext>b</mml:mtext></mml:msubsup></mml:mrow></mml:math> <tex-math>M_{\rm{v}}^{\rm{b}}</tex-math> </alternatives></inline-formula>-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.</p> </abstract>ARTICLEtrue note on convolution of Janowski type functions with q-derivative<abstract> <title style='display:none'>Abstract</title> <p>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 𝒮<sub>q</sub>(A, B, α).</p> </abstract>ARTICLEtrue family of bi-univalent functions with respect to symmetric conjugate points associated with Borel distribution<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we introduce and investigate a new family, denoted by 𝒲<sub>Σ</sub><sup>sc</sup> (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.</p> </abstract>ARTICLEtrue of analytic functions with negative coefficients related with Miller-Ross-type Poisson distribution series<abstract> <title style='display:none'>Abstract</title> <p>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 𝒲<sub>δ</sub>(α, γ, β) of analytic functions with negative coefficients .Also, we investigate several inclusion properties of the classes 𝒮<sup>∗</sup>, 𝒦 and ℝ<sup>τ</sup>(A, B) associated of the operator 𝕀<sub>ν,c</sub><sup>m</sup> 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.</p> </abstract>ARTICLEtrue Menelaus’ and Ceva’s theorems in Nil geometry<abstract> <title style='display:none'>Abstract</title> <p>In this paper we deal with <bold>Nil</bold> 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 <bold>Nil</bold> space. In our work we will use the projective model of <bold>Nil</bold> geometry described by E. Molnár in [<xref ref-type="bibr" rid="j_ausm-2023-0008_ref_006">6</xref>].</p> </abstract>ARTICLEtrue a new p(x)-Kirchhoff type problems with p(x)-Laplacian-like operators and Neumann boundary conditions<abstract> <title style='display:none'>Abstract</title> <p>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<sub>+</sub>) 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.</p> </abstract>ARTICLEtrue new results on the prime order Cayley graph of given groups<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we study the prime order Cayley graph assigned to the group ℤ<sub>n</sub> 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 ℤ<sub>n</sub> and 𝒟<sub>2n</sub>.</p> </abstract>ARTICLEtrue convex functions and some integral inequalities on domains from plane<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue, generalizations and analogs of Menon’s identity: a survey<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue uniform numerical method for singularly perturbed differential equations having both small and large delay<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue the strong approximation of the non-overlapping k-spacings process with application to the moment convergence rates<abstract> <title style='display:none'>Abstract</title> <p>In the present work, we establish the strong approximations of the empirical k-spacings process {α<sub>n</sub>(x): 0 ≤ x&lt; ∞} (cf. (3)). We state the moment convergence rates results for this process.</p> </abstract>ARTICLEtrue another Euclidean plane exist other than the parasphere?<abstract><title style='display:none'>Abstract</title><p>It is shown that for the question of the title the answer is yes. We construct a plane in the hyperbolic space which is Euclidean.</p></abstract>ARTICLEtrue