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

We contribute to the development of equivalence of fixed point iterative sequences for multivalued mappings in modular function spaces, by proving the equivalence of convergence of implicit Mann, implicit Ishikawa, implicit Noor, implicit multistep iterative sequences for multivalued ρ− quasi-contractive-like mapppings in modular function spaces. An example is provided to support the applicability of the results. This work is complementary to equivalence results on normed and metric spaces in the literature.
</abstract>

Fixed point theorems and equivalence results for classes of multivalued mappings in modular function spaces

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

The intention of this article is to introduce and characterise the concept of preopen sets and prelocally closed sets in Generalised Topology and Minimal structure spaces.
</abstract>

Preopen sets and prelocally closed sets in generalised topology and minimal structure spaces

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

This paper is concerned with the analysis of an infinite-capacity batch arrival multi-server queueing system with Bernoulli feedback, synchronous multiple and single working vacation policies, waiting servers, reneging and retention of reneged customers. The steady-state solution of the queueing system is obtained by using probability generating function (PGF). In addition, important performance measures of the queueing system are derived. Then, a cost model is formulated in order to carry out the parameter optimization using genetic algorithm (GA). Finally, numerical study is presented in which various system performance measures are evaluated based on supposed numerical values given to the system parameters.
</abstract>

Djillali Liabes University of Sidi Bel Abbes

University of Sidi Bel Abbes, Ecole Supérieure En Sciences Appliquées

Laboratory of Stochastic Models, Statistic and Applications

Analysis of a batch arrival multi-server queueing system with waiting servers, synchronous working vacations and impatient customers

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

This paper aims to show how some standard general results can be used to uncover the spectral theory of tridiagonal and related matrices more elegantly and simply than existing approaches. As a typical example, we apply the theory to the special tridiagonal matrices in recent papers on orthogonal polynomials arising from Jordan blocks. Consequently, we find that the polynomials and spectral theory of the special matrices are expressible in terms of the Chebyshev polynomials of second kind, whose properties yield interesting results. For special cases, we obtain results in terms of the Fibonacci numbers and Legendre polynomials.
</abstract>

Doha District, Safat 13133, Kuwait and Chair of Computational Mathematics, University of Deusto

On tridiagonal matrices associated with Jordan blocks

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

This paper studies the existence of periodic solutions of a third order iterative differential equation. The main tool used here is Krasnoselskii-Burton’s fixed point theorem dealing with a sum of two mappings, one is a large contraction and the other is compact.
</abstract>

Department of Mathematics and Informatics

Study of periodic solutions for third-order iterative differential equations via Krasnoselskii-Burton’s theorem

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

This article shows the existence and multiplicity of weak solutions for the singular subelliptic system on the Heisenberg group
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2022-0006_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mo>{</mo> <mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><mo>-</mo><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><msup><mrow><mi>ℍ</mi></mrow><mi>n</mi></msup></mrow></msub><mi>u</mi><mo>+</mo><mi>a</mi><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow><mfrac><mi>u</mi><mrow><msup><mrow><mrow><mrow><mo>(</mo><mrow><msup><mrow><mrow><mrow><mo>|</mo> <mi>z</mi> <mo>|</mo></mrow></mrow></mrow><mn>4</mn></msup><mo>+</mo><msup><mrow><mi>t</mi></mrow><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></msup></mrow></mfrac><mo>=</mo><mi>λ</mi><msub><mrow><mi>F</mi></mrow><mi>u</mi></msub><mrow><mo>(</mo><mrow><mi>ξ</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi></mrow><mo>)</mo></mrow></mrow></mtd><mtd columnalign="left"><mrow><mi>i</mi><mi>n</mi><mi> </mi><mi> </mi><mi> </mi><mi mathvariant="normal">Ω</mi><mo>,</mo></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow><mo>-</mo><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><msup><mrow><mi>ℍ</mi></mrow><mi>n</mi></msup></mrow></msub><mi>v</mi><mo>+</mo><mi>b</mi><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow><mfrac><mi>v</mi><mrow><msup><mrow><mrow><mrow><mo>(</mo><mrow><msup><mrow><mrow><mrow><mo>|</mo> <mi>z</mi> <mo>|</mo></mrow></mrow></mrow><mn>4</mn></msup><mo>+</mo><msup><mrow><mi>t</mi></mrow><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></msup></mrow></mfrac><mo>=</mo><mi>λ</mi><msub><mrow><mi>F</mi></mrow><mi>v</mi></msub><mrow><mo>(</mo><mrow><mi>ξ</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi></mrow><mo>)</mo></mrow></mrow></mtd><mtd columnalign="left"><mrow><mi>i</mi><mi>n</mi><mi> </mi><mi> </mi><mi> </mi><mi mathvariant="normal">Ω</mi><mo>,</mo></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow><mi>u</mi><mo>=</mo><mi>v</mi><mo>=</mo><mn>0</mn></mrow></mtd><mtd columnalign="left"><mrow><mi>o</mi><mi>n</mi><mi> </mi><mi> </mi><mo>∂</mo><mi mathvariant="normal">Ω</mi><mo>.</mo></mrow></mtd></mtr></mtable></mrow> </mrow></mrow></math>
<tex-math>\left\{ {\matrix{ { - {\Delta _{{\mathbb{H}^n}}}u + a\left( \xi \right){u \over {{{\left( {{{\left| z \right|}^4} + {t^2}} \right)}^{{1 \over 2}}}}} = \lambda {F_u}\left( {\xi ,u,v} \right)} \hfill &amp; {in\,\,\,\Omega ,} \hfill \cr { - {\Delta _{{\mathbb{H}^n}}}v + b\left( \xi \right){v \over {{{\left( {{{\left| z \right|}^4} + {t^2}} \right)}^{{1 \over 2}}}}} = \lambda {F_v}\left( {\xi ,u,v} \right)} \hfill &amp; {in\,\,\,\Omega ,} \hfill \cr {u = v = 0} \hfill &amp; {on\,\,\partial \Omega .} \hfill \cr } } \right.</tex-math>
</alternatives>
</disp-formula>
The approach is based on variational methods.
</abstract>

Department of Pure Mathematics, Faculty of Science

Existence results of infinitely many weak solutions of a singular subelliptic system on the Heisenberg group

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

In this paper, we deduce the form of a nonconstant meromorphic function f when some power of f shares certain set counting multiplicities in the weak sense with the k-th derivative of the power. The results of this paper generalize the results due to Lahiri and Zeng [Afr. Mat. 27 (2016), 941-947].
</abstract>

A power of a meromorphic function sharing a set with its higher order derivative

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

For given unit vectors x1, · · ·, xn of a real Banach space E, we define
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2022-0008_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>N</mi><mi>A</mi><mrow><mo>(</mo><mrow><mi>ℒ</mi><mrow><mo>(</mo><mrow><msup><mrow></mrow><mi>n</mi></msup><mi>E</mi></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><msub><mrow><mi>x</mi></mrow><mn>1</mn></msub><mo>,</mo><mo>…</mo><msub><mrow><mi>x</mi></mrow><mi>n</mi></msub></mrow><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo> <mrow><mi>T</mi><mo>∈</mo><mi>ℒ</mi><mrow><mo>(</mo><mrow><msup><mrow></mrow><mi>n</mi></msup><mi>E</mi></mrow><mo>)</mo></mrow><mo>:</mo><mrow><mo>|</mo> <mrow><mi>T</mi><mrow><mo>(</mo><mrow><msub><mrow><mi>x</mi></mrow><mn>1</mn></msub><mo>,</mo><mo>…</mo><msub><mrow><mi>x</mi></mrow><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow> <mo>|</mo></mrow><mo>=</mo><mrow><mo>‖</mo> <mi>T</mi> <mo>‖</mo></mrow><mo>=</mo><mn>1</mn></mrow> <mo>}</mo></mrow><mo>,</mo></mrow></math>
<tex-math>NA\left( {\mathcal{L}\left( {^nE} \right)} \right)\left( {{x_1}, \ldots {x_n}} \right) = \left\{ {T \in \mathcal{L}\left( {^nE} \right):\left| {T\left( {{x_1}, \ldots {x_n}} \right)} \right| = \left\| T \right\| = 1} \right\},</tex-math>
</alternatives>
</disp-formula>
where ℒ(nE) denotes the Banach space of all continuous n-linear forms on E endowed with the norm ||T|| = sup||xk||=1,1≤k≤n |T(x1, . . ., xn)|.
In this paper, we classify NA(ℒ(2l12))((x1, x2), (y1, y2)) for unit vectors (x1, x2), (y1, y2)∈ l12, where l12 = ℝ2 with the l1-norm.
</abstract>

Norm attaining bilinear forms on the plane with the <italic>l</italic>1-norm

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

This current work is presented to deal with the model of double diffusive convection in porous material with variable viscosity, such that the equations for convective fluid motion in a Brinkman type are analysed when the viscosity varies with temperature quadratically. Hence, we carefully find a priori bounds when the coe cients depend only on the geometry of the problem, initial data, and boundary data, where this shows the continuous dependence of the solution on changes in the viscosity. A convergence result is also showen when the variable viscosity is allowed to tend to a constant viscosity.
</abstract>

Department of Mathematics, College of Education for Pure Sciences

Continuous dependence for double diffusive convection in a Brinkman model with variable viscosity

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

In this paper, we define a distance d on the set ℳ of bivariate means. We show that (ℳ, d) is a bounded complete metric space which is not compact. Other algebraic and topological properties of (ℳ, d) are investigated as well.
</abstract>

Department of Mathematics, Faculty of Science

On a metric topology on the set of bivariate means

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

We show that certain known or new inequalities for the logarithm of circular hyperbolic functions imply bounds for exp(±x2) proved in [1].
</abstract>

On logarithm of circular and hyperbolic functions and bounds for exp(±x2)

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

In this paper, semisimple semigroups, duo semigroups, right (left) zero semigroups, right (left) simple semigroups, semilattice of left (right) simple semigroups, semilattice of left (right) groups and semilattice of groups are characterized in terms of soft intersection semigroups, soft intersection ideals of semigroups. Moreover, soft normal semigroups are defined and some characterizations of semigroups with soft normality are given.
</abstract>

Department of Mathematics and Science Education

Analysis of semigroups with soft intersection ideals

AHEAD OF PRINT

Volume 15 (2023): Issue 2 (December 2023)

Volume 15 (2023): Issue 1 (November 2023)

Volume 14 (2022): Issue 2 (December 2022)

Volume 14 (2022): Issue 1 (November 2022)

Volume 13 (2021): Issue 2 (December 2021)

Volume 13 (2021): Issue 1 (August 2021)

Volume 12 (2020): Issue 2 (November 2020)

Volume 12 (2020): Issue 1 (July 2020)

Volume 11 (2019): Issue 2 (December 2019)

Volume 11 (2019): Issue 1 (August 2019)

Volume 10 (2018): Issue 2 (December 2018)

Volume 10 (2018): Issue 1 (August 2018)

Volume 9 (2017): Issue 2 (December 2017)

Volume 9 (2017): Issue 1 (August 2017)

Volume 8 (2016): Issue 2 (December 2016)

Volume 8 (2016): Issue 1 (August 2016)

Volume 7 (2015): Issue 2 (December 2015)

Volume 7 (2015): Issue 1 (October 2015)

Volume 6 (2014): Issue 1 (October 2014)

Volume 5 (2013): Issue 2 (December 2013)

Volume 5 (2013): Issue 1 (February 2013)

Acta Universitatis Sapientiae, Mathematica

 The Acta Universitatis Sapientiae Mathematica publishes original papers in English in all fields of mathematics.   Why subscribe and read   We publish original high quality papers.   Why submit   This is a general audience journal and we offer publication in a wide range of different topics with each article being peer reviewed.   Rejection Rate     70%. Every article undergoes a thorough review process and we publish only the prominent scientific results       Target Group   - researchers in all fields of mathematics.   Archiving   Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.   Plagiarism Policy   The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.   Article Processing Charge (APC)   The journal does not have article processing charges (APCs) nor article submission charges. 