https://www.ajol.info/index.php/qm/issue/feed Quaestiones Mathematicae 2021-02-01T14:11:56+00:00 Publishing Manager publishing@nisc.co.za Open Journal Systems <p><em>Quaestiones Mathematicae</em> is devoted to research articles from a wide range of mathematical areas. Longer expository papers of exceptional quality are also considered. Published in English, the journal receives contributions from authors around the globe and serves as an important reference source for anyone interested in mathematics.</p><p>Read more about the journal <a href="http://www.nisc.co.za/products/12/journals/quaestiones-mathematicae" target="_blank">here</a>. </p> https://www.ajol.info/index.php/qm/article/view/203426 Meromorphic function sharing entire functions IM with its first derivative 2021-02-01T12:18:31+00:00 Sujoy Majumder sm05math@gmail.com Jeet Sarkar sarkar.jeet05@gmail.com <p>In this paper, we use the idea of normal family to investigate the problem of meromorphic function having finitely many poles that share entire functions IM with its first derivative.</p> <p><em>Mathematics Subject Classification (2010):</em> Primary 30D35; Secondary 30D30.</p> 2021-02-01T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/203429 Multiplicative *-Lordan type higher derivations on Von Neumann algebras 2021-02-01T13:06:30+00:00 Bilal Ahmad Wani bilalwanikmr@gmail.com Mohammed Ashraf mashraf80@hotmail.com Wenhui Lin haotienwei@hotmail.com <p>Let&nbsp;<span class="NLM_inline-graphic"><img src="https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/tqma20/2020/tqma20.v043.i12/16073606.2019.1649734/20201222/images/medium/tqma_a_1649734_ilg0001.gif" alt=""></span>&nbsp;be a von Neumann algebra without nonzero central abelian projections on a complex Hilbert space&nbsp;<span class="NLM_inline-graphic"><img src="https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/tqma20/2020/tqma20.v043.i12/16073606.2019.1649734/20201222/images/medium/tqma_a_1649734_ilg0002.gif" alt=""></span>. Let&nbsp;<em>p<sub>n</sub>&nbsp;</em>(<em>X</em>&nbsp;<sub>1</sub>&nbsp;<em>, X</em>&nbsp;<sub>2</sub>&nbsp;<em>, · · ·, X<sub>n</sub>&nbsp;</em>) be the polynomial defined by&nbsp;<em>n</em>&nbsp;indeterminates&nbsp;<em>X</em>&nbsp;<sub>1</sub>, · · ·,&nbsp;<em>X<sub>n</sub>&nbsp;</em>and their Jordan multiple ∗-products. In this paper it is shown that a family&nbsp;<em>𝒟</em>&nbsp;= {<em>d<sub>m</sub>&nbsp;</em>}<em>&nbsp;<sub>m</sub>&nbsp;</em><sub>∈ℕ</sub>&nbsp;of mappings&nbsp;<span class="NLM_inline-graphic"><img src="https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/tqma20/2020/tqma20.v043.i12/16073606.2019.1649734/20201222/images/medium/tqma_a_1649734_ilg0003.gif" alt=""></span>&nbsp;such that&nbsp;<span class="NLM_inline-graphic"><img src="https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/tqma20/2020/tqma20.v043.i12/16073606.2019.1649734/20201222/images/medium/tqma_a_1649734_ilg0004.gif" alt=""></span>, the identity map on&nbsp;<span class="NLM_inline-graphic"><img src="https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/tqma20/2020/tqma20.v043.i12/16073606.2019.1649734/20201222/images/medium/tqma_a_1649734_ilg0001.gif" alt=""></span>&nbsp;satisfies the condition</p> <p><span class="NLM_inline-graphic"><img src="https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/tqma20/2020/tqma20.v043.i12/16073606.2019.1649734/20201222/images/medium/tqma_a_1649734_ilg0005.gif" alt=""></span></p> <p>for all&nbsp;<em>U</em>&nbsp;<sub>1</sub>&nbsp;<em>, U</em>&nbsp;<sub>2</sub>&nbsp;<em>, · · ·, U<sub>n</sub>&nbsp;∈</em>&nbsp;<span class="NLM_inline-graphic"><img src="https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/tqma20/2020/tqma20.v043.i12/16073606.2019.1649734/20201222/images/medium/tqma_a_1649734_ilg0001.gif" alt=""></span>&nbsp;and for each&nbsp;<em>m</em>&nbsp;∈ ℕ if and only if&nbsp;<em>𝒟</em>&nbsp;= {<em>d<sub>m</sub>&nbsp;</em>}<em>&nbsp;<sub>m</sub>&nbsp;</em><sub>∈ℕ</sub>&nbsp;is an additive ∗-higher derivation.</p> <p><em>Mathematics Subject Classification (2010):</em> 47B47, 16W25, 46K15.</p> <p>&nbsp;</p> 2021-02-01T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/203435 Uniform difference method for singularly pertubated delay Sobolev problems 2021-02-01T13:19:30+00:00 Akbar Barati Chiyanesh baratiakbar@yahoo.com Hakki Durus hakkiduru@gmail.com <p>In this paper, a numerical study is made of an initial-boundary value problem for a singularly perturbed delay Sobolev equations (SPDSEs). Here we propose an exponentially fitted method based on finite differences to solve an SPDSE. An exponentially-fitted difference scheme on a uniform mesh, which is accomplished by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form, is presented. We calculate the fitting parameter for an exponentially fitted finite difference scheme corresponding to the problem and establish an error estimate which shows that the method has order of convergence 2 in space and time, independently of the perturbation parameter to the solution of the problem. The stability of the method is discussed. Numerical experiments are performed to support the theoretical results.</p> <p><em>Mathematics Subject Classification (2010):</em> 65M06.</p> 2021-02-01T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/203436 Spanning paths and cycles in triangle-free graphs 2021-02-01T13:24:48+00:00 P. Mafuta phillipmafuta@gmail.com J. Mushanyu mushanyuj@gmail.com <p>Let G bea triangle-free graph of order n and minimum degree δ &gt; n/3. We will determine all lengths of cycles occurring in G. In particular, the length of a longest cycle or path in G is exactly the value admitted by the independence number of G. This value can be computed in time O(n 2.5) using the matching algorithm of Micali and Vazirani. An easy consequence is the observation that triangle-free non-bipartite graphs with δ⩾38n are hamiltonian.</p> <p><em>Mathematics Subject Classification (2010):</em> 05C05, 05C38, 05C45.</p> 2021-02-01T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/203437 A measure of non-compactness on T 3½ spaces based on Arzelà-Ascoli type theorem 2021-02-01T13:47:40+00:00 Filip Turoboś filip.turobos@gmail.com <p>The purpose of this paper is to generalize the measure of non-compactness for the space of continuous functions over the&nbsp;<em>T</em>&nbsp;<sub>3½</sub>&nbsp;space. Motivated by the generalized Arzelà-Ascoli theorem for Tichonoff space&nbsp;<em>T</em>&nbsp;via Wallman compactifiaction Wall(<em>T</em>), we constuct a measure of non-compactness for the space&nbsp;<em>C<sup>b</sup>&nbsp;</em>(<em>T</em>). We also study some of the properties of this object and give another version of Darbotype theorem, suitable for this particular case.</p> <p><em>Mathematics Subject Classification (2010):</em> 46B50, 47H08, 54D35, 54D80.</p> 2021-02-01T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/203438 Joint discrete universality for periodic zeta-functions. II 2021-02-01T13:52:52+00:00 Antanas Laurinčikas antanas.laurinicikas@mif.vu.lt <p>In the paper, for certain classes of operators&nbsp;<em>F</em>&nbsp;in the space of analytic functions, we prove the discrete universality for compositions&nbsp;<em>F</em>&nbsp;(<em>ζ</em>(<em>s,&nbsp;<u class="uu">α</u>&nbsp;</em>;&nbsp;<em><u class="uu">𝔞</u>,&nbsp;<u class="uu">𝔟</u>&nbsp;</em>)), where&nbsp;<em>ζ</em>(<em>s,&nbsp;<u class="uu">α</u>&nbsp;</em>;&nbsp;<em><u class="uu">𝔞</u>&nbsp;</em>;&nbsp;<em><u class="uu">𝔟</u>&nbsp;</em>) is a collection consisting from periodic and periodic Hurwitz zeta-functions, i. e., the approximation of analytic functions by discrete shifts&nbsp;<em>F</em>&nbsp;(<em>ζ</em>(<em>s</em>&nbsp;+&nbsp;<em>ikh,&nbsp;<u class="uu">α</u>&nbsp;</em>;&nbsp;<em><u class="uu">𝔞</u>&nbsp;</em>;&nbsp;<em><u class="uu">𝔟</u>&nbsp;</em>)) with&nbsp;<em>h &gt;</em>&nbsp;0 and&nbsp;<em>k</em>&nbsp;= 0, 1, . . . . For this, a theorem of [12] is applied.</p> <p><em>Mathematics Subject Classification (2010):</em> Primary: 11M41; Secondary: 41A30.</p> 2021-02-01T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/203439 On polynomial equation rings and radicals 2021-02-01T13:58:11+00:00 D.I.C. Mendes imendes@ubi.pt B. Ochirbat ochirbat@must.edu.mn S. Tumurbat stumurbat@hotmail.com <p>The notion of&nbsp;<em>n</em>-polynomial equation ring, for an arbitrary but fixed positive integer&nbsp;<em>n</em>, is introduced. A ring A is called an&nbsp;<em>n</em>- polynomial equation ring if&nbsp;<em>γ</em>(<em>A</em>[<em>X<sub>n</sub>&nbsp;</em>]) =&nbsp;<em>γ</em>(<em>A</em>)[&nbsp;<em>X<sub>n</sub>&nbsp;</em>], for all radicals&nbsp;<em>γ</em>. If this equation holds for all hereditary radicals&nbsp;<em>γ</em>, then&nbsp;<em>A</em>&nbsp;is said to be a hereditary&nbsp;<em>n</em>-polynomial equation ring. Various characterizations of these rings are provided. It is shown that, for any ring&nbsp;<em>A</em>, the zero-ring on the additive group of A is an&nbsp;<em>n</em>- polynomial equation ring and that any Baer radical ring is a hereditary&nbsp;<em>n</em>- polynomial equation ring. New radicals based on these notions are introduced, one of which is a special radical with a polynomially extensible semisimple class.</p> <p><em>Mathematics Subject Classification (2010):</em> 16N80.</p> <p>&nbsp;</p> 2021-02-01T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/203440 Approximate best proximity point sequences for C*λ mappings in strictly convex Banach spaces 2021-02-01T14:07:53+00:00 M. Gabeleh Gabeleh@abru.ac.ir S.P. Moshokoa moshokoasp@tut.ac.za O. Olela Otafudu olivier.olelaotafudu@wits.ac.za <p>Let&nbsp;<em>A</em>&nbsp;and&nbsp;<em>B</em>&nbsp;be nonempty subsets of a Banach space&nbsp;<em>X</em>&nbsp;and&nbsp;<em>T</em>&nbsp;:&nbsp;<em>A</em>&nbsp;→&nbsp;<em>B</em>&nbsp;be a non-self mapping. An approximate sequence of best proximity points for the mapping&nbsp;<em>T</em>&nbsp;is a sequence {<em>x<sub>n</sub>&nbsp;</em>} in A such that lim<em>&nbsp;<sub>n</sub>&nbsp;</em><sub>→∞</sub>&nbsp;||&nbsp;<em>x<sub>n</sub>&nbsp;</em>−&nbsp;<em>T x<sub>n</sub>&nbsp;</em>|| → dist(<em>A</em>,&nbsp;<em>B</em>). In the current paper, we survey the existence of approximate best proximity point sequences for single and multivalued&nbsp;<span class="NLM_inline-graphic"><img src="https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/tqma20/2020/tqma20.v043.i12/16073606.2019.1655109/20201222/images/medium/tqma_a_1655109_ilg0001.gif" alt=""></span>&nbsp;non-self mappings in strictly convex Banach spaces. We also introduce a geometric notion on a nonempty and convex pair of subsets of a Banach space, called semi-Opial condition, and establish some new best proximity point theorems.</p> <p><em>Mathematics Subject Classification (2010):</em> 47H10, 47H09, 46B20.</p> 2021-02-01T00:00:00+00:00 Copyright (c)