<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

Department of Applied, Sciences & Humanities

On k-semi-centralizing maps of generalized matrix algebras

<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

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

<abstract xmlns="http://www.w3.org/1999/xhtml">

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 <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0013_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mtext>K</mtext></mrow><mtext>n</mtext><mtext>T</mtext></msubsup><mo>=</mo><msubsup><mo>∑</mo><mrow><mtext>k</mtext><mo>=</mo><mn>1</mn></mrow><mtext>n</mtext></msubsup><mrow><msub><mrow><mtext>t</mtext></mrow><mrow><mtext>k</mtext><mo>,</mo><mtext>n</mtext></mrow></msub><msub><mrow><mtext>D</mtext></mrow><mtext>k</mtext></msub></mrow></mrow></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 Dk is the kth Dirichlet kernel) satisfy
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0013_eq_002.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msub><mrow><mrow><mrow><mo>‖</mo><mrow><msubsup><mrow><mtext>K</mtext></mrow><mtext>n</mtext><mtext>T</mtext></msubsup></mrow><mo>‖</mo></mrow></mrow></mrow><mn>1</mn></msub><mo>≤</mo><mtext>c</mtext><mtext>.</mtext></mrow></math>
<tex-math>{\left\| {{\rm{K}}_{\rm{n}}^{\rm{T}}} \right\|_1} \le {\rm{c}}{\rm{.}}</tex-math>
</alternatives>
</disp-formula>
As a result of this we prove that for any 1 <italic>≤</italic> p &lt; ∞ and f ∈ Lp the Lp-norm convergence <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0013_eq_003.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mo>∑</mo><mrow><mtext>k</mtext><mo>=</mo><mn>1</mn></mrow><mtext>n</mtext></msubsup><mrow><msub><mrow><mtext>t</mtext></mrow><mrow><mtext>k</mtext><mo>,</mo><mtext>n</mtext></mrow></msub><msub><mrow><mtext>S</mtext></mrow><mtext>k</mtext></msub><mrow><mo>(</mo><mtext>f</mtext><mo>)</mo></mrow></mrow><mo>→</mo><mtext>f</mtext></mrow></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.
</abstract>

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

<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

Department of Engineering Mathematics, Faculty of Engineering

Department of Mathematics, Faculty of Arts and Sciences

Oscillatory behavior of second-order nonlinear noncanonical neutral differential equations

<abstract xmlns="http://www.w3.org/1999/xhtml">

The aim is to utilize a new metric called an <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0015_eq_002.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>M</mi></mrow><mtext>v</mtext><mtext>b</mtext></msubsup></mrow></math>
<tex-math>M_{\rm{v}}^{\rm{b}}</tex-math>
</alternatives>
</inline-formula>–metric which is an improvement and generalization of Mv−metric to revisit the celebrated Banach and Sehgal contractions in <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0015_eq_003.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>M</mi></mrow><mtext>v</mtext><mtext>b</mtext></msubsup></mrow></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="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0015_eq_004.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>M</mi></mrow><mtext>v</mtext><mtext>b</mtext></msubsup></mrow></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.
</abstract>

Fixed point in <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0015_eq_001.png"/>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>ℳ</mi></mrow><mtext>v</mtext><mtext>b</mtext></msubsup></mrow></math>
<tex-math>M_{\rm{v}}^{\rm{b}}</tex-math>
</alternatives>
</inline-formula>– metric space and applications

<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

Automorphisms of Zappa-Szép product fixing a subgroup

<abstract xmlns="http://www.w3.org/1999/xhtml">

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="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0017_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mtext>f</mtext><mrow><mo>(</mo><mtext>z</mtext><mo>)</mo></mrow><mo>=</mo><mtext>z</mtext><mo>+</mo><msubsup><mo>∑</mo><mrow><mtext>n</mtext><mo>=</mo><mn>2</mn></mrow><mo>∞</mo></msubsup><mrow><msub><mrow><mi>α</mi></mrow><mtext>n</mtext></msub><msup><mrow><mtext>z</mtext></mrow><mtext>n</mtext></msup></mrow></mrow></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 |α5| − |α4|.
</abstract>

Department of Mathematics, Faculty of Civil Engineering

Department of Mathematics and Informatics, Faculty of Mechanical Engineering

Ss. Cyril and Methodius University in Skopje

Two applications of Grunsky coefficients in the theory of univalent functions

<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

Pt. L. M. S. Campus, Sri Dev Suman Uttarakhand University

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

<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

Department of Mathematics, Faculty of Engineering and Natural Sciences

Department of Mathematics, Faculty of Arts and Science

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

AHEAD OF PRINT

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Acta Universitatis Sapientiae, Mathematica

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