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Arabian Journal of Mathematics最新文献

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Classification of additive mappings on certain rings and algebras 某些环和代数上的加法映射分类
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-11-14 DOI: 10.1007/s40065-023-00448-7
Abu Zaid Ansari
{"title":"Classification of additive mappings on certain rings and algebras","authors":"Abu Zaid Ansari","doi":"10.1007/s40065-023-00448-7","DOIUrl":"10.1007/s40065-023-00448-7","url":null,"abstract":"<div><p>The objective of this research is to prove that an additive mapping <span>(Delta :{mathcal {A}}rightarrow {mathcal {A}})</span> will be a generalized derivation associated with a derivation <span>(partial :{mathcal {A}}rightarrow {mathcal {A}})</span> if it satisfies the following identity <span>(Delta (r^{m+n+p})=Delta (r^m)r^{n+p}+r^mpartial (r^{n})r^p+r^{m+n}partial (r^p))</span> for all <span>(rin {mathcal {A}})</span>, where <span>(m, nge 1)</span> and <span>(pge 0)</span> are fixed integers and <span>({mathcal {A}})</span> is a semiprime ring. Another analogous has been done where an additive mapping behaves like a generalized left derivation associated with a left derivation on <span>({mathcal {A}})</span> satisfying certain algebraic identity. The proofs of these advancements are derived employing algebraic concepts. These theorems have been validated by offering an example that shows they are not insignificant. Furthermore, we provide an application in the framework of Banach algebra.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"35 - 43"},"PeriodicalIF":0.9,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00448-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134900847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Calculus of variations with higher order Caputo fractional derivatives 带有高阶卡普托分数导数的变动微积分
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-10-30 DOI: 10.1007/s40065-023-00447-8
Rui A. C. Ferreira
{"title":"Calculus of variations with higher order Caputo fractional derivatives","authors":"Rui A. C. Ferreira","doi":"10.1007/s40065-023-00447-8","DOIUrl":"10.1007/s40065-023-00447-8","url":null,"abstract":"<div><p>In this work, we consider fractional variational problems depending on higher order fractional derivatives. We obtain optimality conditions for such problems and we present and discuss some examples. We conclude with possible research directions.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"91 - 101"},"PeriodicalIF":0.9,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00447-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136106395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Best approximation with geometric constraints 带几何约束的最佳近似值
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-09-29 DOI: 10.1007/s40065-023-00446-9
Hossein Mohebi, Hassan Bakhtiari
{"title":"Best approximation with geometric constraints","authors":"Hossein Mohebi,&nbsp;Hassan Bakhtiari","doi":"10.1007/s40065-023-00446-9","DOIUrl":"10.1007/s40065-023-00446-9","url":null,"abstract":"<div><p>In this paper, we consider a finite family of sets (geometric constraints) <span>(F_{1}, F_{2},ldots , F_{r})</span> in the Euclidean space <span>({mathbb {R}}^n.)</span> We show under mild conditions on the geometric constraints that the “perturbation property” of the constrained best approximation from a nonempty closed set <span>(K cap F)</span> is characterized by the “convex conical hull intersection property” (CCHIP in short) at a reference feasible point in <i>F</i>. In this case, <i>F</i> is the intersection of the geometric constraints <span>(F_{1}, F_{2},ldots , F_{r},)</span> and <i>K</i> is a nonempty closed convex set in <span>({mathbb {R}}^n)</span> such that <span>(K cap F ne emptyset .)</span> We do this by first proving a dual cone characterization of the contingent cone of the set <i>F</i>. Finally, we obtain the “Lagrange multiplier characterizations” of the constrained best approximation. Several examples are given to illustrate and clarify our results.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"163 - 180"},"PeriodicalIF":0.9,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00446-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135133101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integral transforms suitable for solving fractional differential equations 适合求解分数微分方程的积分变换
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-09-23 DOI: 10.1007/s40065-023-00445-w
Chiara Boiti, Jonathan Franceschi
{"title":"Integral transforms suitable for solving fractional differential equations","authors":"Chiara Boiti,&nbsp;Jonathan Franceschi","doi":"10.1007/s40065-023-00445-w","DOIUrl":"10.1007/s40065-023-00445-w","url":null,"abstract":"<div><p>The purpose of this article is to obtain appropriate tools for solving fractional differential equations that are flexible enough to adapt to different purposes. We thus look for a very general fractional Fourier transform with a phase function which can be appropriately chosen according to the problem you want to face.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"79 - 89"},"PeriodicalIF":0.9,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00445-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135966676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A nonlocal type problem involving a mixed local and nonlocal operator 涉及混合局部和非局部算子的非局部类型问题
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-09-22 DOI: 10.1007/s40065-023-00444-x
Kheireddine Biroud
{"title":"A nonlocal type problem involving a mixed local and nonlocal operator","authors":"Kheireddine Biroud","doi":"10.1007/s40065-023-00444-x","DOIUrl":"10.1007/s40065-023-00444-x","url":null,"abstract":"<div><p>In this paper, we consider the nonlocal elliptic problem involving a mixed local and nonlocal operator, </p><div><div><span>$$begin{aligned} (P)left{ begin{array}{rcll} left( displaystyle int limits _Omega f(x,u)dxright) ^{beta }mathfrak {L_{p,s}}(u)&amp;{}= &amp;{} f^alpha (x,u) &amp;{} text { in }Omega , u &amp;{}&gt; &amp;{} 0 &amp;{} text {in }Omega , u &amp;{} = &amp;{} 0 &amp;{} text {in }{mathbb {R}}^N setminus Omega , end{array} right. end{aligned}$$</span></div></div><p>where <span>(Omega subset {mathbb {R}}^N)</span> is a bounded regular domain, <span>(mathfrak {L_{p,s}}equiv -Delta _p+(-Delta )^s_p)</span>, <span>(0&lt;s&lt;1&lt;p&lt;N)</span>, <span>(alpha ,,beta in {mathbb {R}})</span> and <span>(f: Omega times {mathbb {R}}rightarrow {mathbb {R}})</span> be a nonnegative function which is defined almost everywhere with respect to the variable <i>x</i>. Using Schauder and Tychonoff fixed point theorems, we get two existence theorems of weak positive solutions under some hypothesis on <span>(alpha , beta )</span> and <i>f</i>.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"63 - 78"},"PeriodicalIF":0.9,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00444-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136011545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Singular two-phase problem on a complete manifold: analysis and insights 完整流形上的奇异两相问题：分析与启示
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-09-12 DOI: 10.1007/s40065-023-00443-y
Omar Benslimane, Ahmed Aberqi
{"title":"Singular two-phase problem on a complete manifold: analysis and insights","authors":"Omar Benslimane,&nbsp;Ahmed Aberqi","doi":"10.1007/s40065-023-00443-y","DOIUrl":"10.1007/s40065-023-00443-y","url":null,"abstract":"<div><p>We focus on two-phase problems with singular and superlinear parametric terms on the right-hand side. Using fibering maps and the Nehari manifold method, we prove that there are at least two non-trivial positive solutions in a geometric setting that is locally similar to Euclidean spaces but has different global properties for all except the smallest values of parameter <span>(mu &gt; 0.)</span> Singularities may appear at discrete locations in the manifold, which is a challenge for the work due to the unpredictable behavior of the solution. The findings presented here generalize some known results.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"45 - 62"},"PeriodicalIF":0.9,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00443-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135879132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
System of generalized variational-like inclusions involving (varvec{(P,eta )})-accretive mapping and fixed point problems in real Banach spaces 实巴纳赫空间中涉及(varvec{(P,ea )})-accretive mapping和定点问题的广义变分样结论系统
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-08-30 DOI: 10.1007/s40065-023-00440-1
Javad Balooee, Suliman Al-Homidan
{"title":"System of generalized variational-like inclusions involving (varvec{(P,eta )})-accretive mapping and fixed point problems in real Banach spaces","authors":"Javad Balooee,&nbsp;Suliman Al-Homidan","doi":"10.1007/s40065-023-00440-1","DOIUrl":"10.1007/s40065-023-00440-1","url":null,"abstract":"<div><p>This paper attempts to prove the Lipschitz continuity of the resolvent operator associated with a <span>((P,eta ))</span>-accretive mapping and compute an estimate of its Lipschitz constant. This is done under some new appropriate conditions that are imposed on the parameter and mappings involved in it; with the goal of approximating a common element of the solution set of a system of generalized variational-like inclusions and the fixed point set of a total asymptotically nonexpansive mapping in the framework of real Banach spaces. A new iterative algorithm based on the resolvent operator technique is proposed. Under suitable conditions, we prove the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the two sets mentioned above. The final section is dedicated to investigating and analyzing the notion of a generalized <i>H</i>(., .)-accretive mapping introduced and studied by Kazmi et al. (Appl Math Comput 217:9679–9688, 2011). In this section, we provide some comments based on the relevant results presented in their work.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"1 - 33"},"PeriodicalIF":0.9,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00440-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82951209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamical analysis of a discrete-time plant–herbivore model 离散时间植物食草动物模型的动态分析
IF 0.9
Arabian Journal of Mathematics Pub Date : 2023-08-29 DOI: 10.1007/s40065-023-00442-z
M. Y. Hamada
{"title":"Dynamical analysis of a discrete-time plant–herbivore model","authors":"M. Y. Hamada","doi":"10.1007/s40065-023-00442-z","DOIUrl":"10.1007/s40065-023-00442-z","url":null,"abstract":"<div><p>In this paper, a discrete-time model of a plant–herbivore system is qualitatively analyzed using difference equations to describe population dynamics over time. The goal is to examine how the model behaves under varying parameter values and initial conditions. Results reveal that the model exhibits diverse dynamical behaviors such as stable equilibria, period-doubling cascade, and chaotic attractors. The analysis indicates that changes in crucial parameters greatly affect the system’s dynamics. This study offers crucial insights into plant–herbivore systems and highlights the value of qualitative analysis in comprehending intricate ecological systems.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"121 - 131"},"PeriodicalIF":0.9,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00442-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75970228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the first integrals of the Painlevé classes of equations 关于Painlevé类方程的第一积分
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-08-27 DOI: 10.1007/s40065-023-00441-0
Mogahid M. A. Ahmed, Bader Alqurashi, Abdul Hamid Kara
{"title":"On the first integrals of the Painlevé classes of equations","authors":"Mogahid M. A. Ahmed,&nbsp;Bader Alqurashi,&nbsp;Abdul Hamid Kara","doi":"10.1007/s40065-023-00441-0","DOIUrl":"10.1007/s40065-023-00441-0","url":null,"abstract":"<div><p>The role of symmetries and first integrals are well known mechanisms for the reduction of ordinary differential equations (odes) and, used in conjunction, lead to double reductions of the odes. In this article, we attempt to construct the first integrals of a large class of the well known second-order Painlevé equations. In some cases, variational and/or gauge symmetries have additional applications following a known Lagrangian in which case the first integral is obtained by Noether’s theorem. Sometimes, it is more convenient to adopt the ‘multiplier’ approach to find the first integrals. In a number of cases, we can conclude that the class is linearizable.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 3","pages":"565 - 571"},"PeriodicalIF":1.2,"publicationDate":"2023-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00441-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50516859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Compact formula for skew-symmetric system of matrix equations 矩阵方程斜对称系统的紧致公式
IF 1.2
Arabian Journal of Mathematics Pub Date : 2023-08-14 DOI: 10.1007/s40065-023-00439-8
Abdur Rehman, Ivan I. Kyrchei
{"title":"Compact formula for skew-symmetric system of matrix equations","authors":"Abdur Rehman,&nbsp;Ivan I. Kyrchei","doi":"10.1007/s40065-023-00439-8","DOIUrl":"10.1007/s40065-023-00439-8","url":null,"abstract":"<div><p>In this paper, we consider skew-Hermitian solution of coupled generalized Sylvester matrix equations encompassing <span>(*)</span>-hermicity over complex field. The compact formula of the general solution of this system is presented in terms of generalized inverses when some necessary and sufficient conditions are fulfilled. An algorithm and a numerical example are provided to validate our findings. A numerical example is carried out using determinantal representations of the Moore–Penrose inverse.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 3","pages":"587 - 600"},"PeriodicalIF":1.2,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00439-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50480116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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