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Geometric properties of generalized Bessel function of arbitrary order and degree 任意阶和阶的广义贝塞尔函数的几何特性
IF 0.9
Afrika Matematika Pub Date : 2024-06-17 DOI: 10.1007/s13370-024-01195-4
Naveen Kumari, Jugal Kishore Prajapat
{"title":"Geometric properties of generalized Bessel function of arbitrary order and degree","authors":"Naveen Kumari,&nbsp;Jugal Kishore Prajapat","doi":"10.1007/s13370-024-01195-4","DOIUrl":"10.1007/s13370-024-01195-4","url":null,"abstract":"<div><p>The Bessel function and its various generalizations have extensively been studied in various branches of applied mathematics and theoretical physics, including the Geometric Function Theory. In this paper, we study basic characteristics of Bessel functions of order <span>(mu )</span> and degree <span>(nu )</span>. Among the results that we investigate are the results giving the characteristic properties of univalence, convexity and starlikeness. We further investigate the conditions under which the function <span>(L_{mu ,nu })</span> are strongly convex and strongly starlike. Several corollaries are also mentioned depicting the usefulness of the main results, one of the Corollary providing improvement in a result for normalized Bessel function.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence results, regularity and compactness properties, in the (alpha )-norm, for semilinear partial functional integrodifferential equations with nonlinear Kernel and delay argument 具有非线性内核和延迟参数的半线性偏函数积分微分方程在 $$alpha $$-规范下的存在性结果、正则性和紧凑性特性
IF 0.9
Afrika Matematika Pub Date : 2024-06-15 DOI: 10.1007/s13370-024-01196-3
Boubacar Diao, Mamadou Sy
{"title":"Existence results, regularity and compactness properties, in the (alpha )-norm, for semilinear partial functional integrodifferential equations with nonlinear Kernel and delay argument","authors":"Boubacar Diao,&nbsp;Mamadou Sy","doi":"10.1007/s13370-024-01196-3","DOIUrl":"10.1007/s13370-024-01196-3","url":null,"abstract":"<div><p>In this paper, we consider a finite delay integro-differential equation with a nonlinear kernel in a general Banach space. The nonlinear part is assumed to be continuous with respect to a fractional power of the linear part in the second variable. We prove, using the semigroup theory, the local existence, continuous dependence of the initial data, the phenomena of blowing up, regularity, and compactness properties of the so-called mild solution. An application is provided to illustrate our results.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141336861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inverse nodal problem with eigenparameter boundary conditions 具有特征参数边界条件的反节点问题
IF 0.9
Afrika Matematika Pub Date : 2024-05-22 DOI: 10.1007/s13370-024-01194-5
Unal Ic, Hikmet Koyunbakan
{"title":"Inverse nodal problem with eigenparameter boundary conditions","authors":"Unal Ic,&nbsp;Hikmet Koyunbakan","doi":"10.1007/s13370-024-01194-5","DOIUrl":"10.1007/s13370-024-01194-5","url":null,"abstract":"<div><p>The reconstruction of potential function using nodal parameters is an inverse problem that has been studied in this work. An efficient and highly helpful transformation allowed for the extraction of a reconstruction formula for the problem’s potential function by a narrow collection of nodal data only. Additionally, the method’s efficacy was shown by a few numerical illustrations.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141109827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On neutral integrodifferential equations with state-dependent delay in Banach spaces 论巴拿赫空间中具有状态相关延迟的中性微分方程
IF 0.9
Afrika Matematika Pub Date : 2024-05-10 DOI: 10.1007/s13370-024-01193-6
Mbarack Fall, Aziz Mané, Ramkumar Kasinathan, Ravikumar Kasinathan, Mamadou Abdoul Diop
{"title":"On neutral integrodifferential equations with state-dependent delay in Banach spaces","authors":"Mbarack Fall,&nbsp;Aziz Mané,&nbsp;Ramkumar Kasinathan,&nbsp;Ravikumar Kasinathan,&nbsp;Mamadou Abdoul Diop","doi":"10.1007/s13370-024-01193-6","DOIUrl":"10.1007/s13370-024-01193-6","url":null,"abstract":"<div><p>In this work, we investigate the existence of mild solution for semilinear integro-differential systems and semilinear neutral integro-differential systems with state-dependent delay in Banach spaces. Using Mönch’s fixed point theorem, the theory of Grimmer’s resolvent operator and the idea of measures of non-compactness, we prove the existence results. At the end, an example is given to further illustrate the conclusions drawn from the theoretical study.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140992324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On approximation by Abel–Poisson and conjugate Abel–Poisson means in Hölder metric 论霍德尔度量中阿贝尔-泊松和共轭阿贝尔-泊松手段的近似值
IF 0.9
Afrika Matematika Pub Date : 2024-05-08 DOI: 10.1007/s13370-024-01190-9
Xhevat Z. Krasniqi
{"title":"On approximation by Abel–Poisson and conjugate Abel–Poisson means in Hölder metric","authors":"Xhevat Z. Krasniqi","doi":"10.1007/s13370-024-01190-9","DOIUrl":"10.1007/s13370-024-01190-9","url":null,"abstract":"<div><p>The degree of approximation (in Hölder metric) of a periodic function belonging to a specific Hölder class by its Abel–Poisson means of Fourier series and of the conjugate function by the conjugate Abel–Poisson means of the conjugate series of the Fourier series is obtained.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141129096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interdependence of additivity and sine additivity 可加性与正弦可加性之间的相互依存关系
IF 0.9
Afrika Matematika Pub Date : 2024-05-06 DOI: 10.1007/s13370-024-01192-7
Bruce Ebanks
{"title":"Interdependence of additivity and sine additivity","authors":"Bruce Ebanks","doi":"10.1007/s13370-024-01192-7","DOIUrl":"10.1007/s13370-024-01192-7","url":null,"abstract":"<div><p>Let <i>S</i> be a semigroup and <i>K</i> a field. A function <span>(f:S rightarrow K)</span> is additive if <span>(f(xy) = f(x) + f(y))</span> for all <span>(x,y in S)</span>, and functions <span>(g,h:S rightarrow K)</span> form a sine pair if they satisfy the sine addition law <span>(g(xy) = g(x)h(y) + h(x)g(y))</span> for all <span>(x,y in S)</span>. Adding these two equations we arrive at the functional equation (*) <span>(f(xy) + g(xy) = f(x) + f(y) + g(x)h(y) + h(x)g(y))</span>. The alienation question for additivity and sine additivity asks whether (*) implies that <i>f</i> is additive and (<i>g</i>, <i>h</i>) is a sine pair. To fully answer this question we find the general solution of (*) for unknown functions <span>(f,g,h:S rightarrow {mathbb {C}})</span>. The solution illustrates a significant amount of interdependence between additivity and sine additivity.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141129529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integral operators and fractional integrals on Cesáro-Morrey function spaces Cesáro-Morrey 函数空间上的积分算子和分数积分
IF 0.9
Afrika Matematika Pub Date : 2024-05-04 DOI: 10.1007/s13370-024-01191-8
Kwok-Pun Ho
{"title":"Integral operators and fractional integrals on Cesáro-Morrey function spaces","authors":"Kwok-Pun Ho","doi":"10.1007/s13370-024-01191-8","DOIUrl":"10.1007/s13370-024-01191-8","url":null,"abstract":"<div><p>In this paper, we extend the study of the Cesáro function spaces to the Cesáro-Morrey function spaces. We establish a general principle on the boundedness of integral operators on the Cesáro-Morrey function spaces. By applying this principle, we have the boundedness of the Erdélyi-Kober fractional integrals and the Hadamard fractional integrals on the Cesáro-Morrey function spaces. In addition, we also extend the study of Tandori spaces to Tandori-Morrey spaces.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141013175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Further bounds for the Euclidean operator radius of a pair of operators and their applications 一对算子的欧氏算子半径的进一步界限及其应用
IF 0.9
Afrika Matematika Pub Date : 2024-04-29 DOI: 10.1007/s13370-024-01189-2
Soumia Aici, Abdelkader Frakis, Fuad Kittaneh
{"title":"Further bounds for the Euclidean operator radius of a pair of operators and their applications","authors":"Soumia Aici,&nbsp;Abdelkader Frakis,&nbsp;Fuad Kittaneh","doi":"10.1007/s13370-024-01189-2","DOIUrl":"10.1007/s13370-024-01189-2","url":null,"abstract":"<div><p>We give several lower and upper bounds for the Euclidean operator radius of two operators on a Hilbert space. We improve some earlier related bounds. Also, as applications of these bounds, we deduce some new bounds for the classical numerical radius. Some of these bounds are refinements of certain existing bounds.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Certain properties of 3D degenerate generalized Fubini polynomials and applications 三维退化广义富比尼多项式的某些性质及其应用
IF 0.9
Afrika Matematika Pub Date : 2024-04-13 DOI: 10.1007/s13370-024-01187-4
Mumtaz Riyasat, Amal S. Alali, Subuhi Khan
{"title":"Certain properties of 3D degenerate generalized Fubini polynomials and applications","authors":"Mumtaz Riyasat,&nbsp;Amal S. Alali,&nbsp;Subuhi Khan","doi":"10.1007/s13370-024-01187-4","DOIUrl":"10.1007/s13370-024-01187-4","url":null,"abstract":"<div><p>A renewed interest in combinatorial and arithmetic properties as well as applications to differential equations, identities, formulas, and probability theory has been sparked by the study of degenerate versions of several specific numbers and polynomials. The article aims to explore a 3D unified degenerate class of generalized Fubini polynomials by utilizing 2D generalized degenerate polynomials. The potential of applications are provided by deriving certain computational formulas and identities,recurrence relations and derivative expressions for the 3D degenerated Gould–Hopper–Fubini, 3D degenerate Hermite-Fubini and 3D degenerate 2-iterated Fubini polynomials, which are extracted out of the 3D degenerate generalized Fubini polynomials. Finally, the behaviour of zeros of two concrete degenerate polynomials with some specific set of parameters is shown by drawing graphs using Mathematica</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inequalities involving the harmonic-arithmetic index 涉及谐波算术指数的不等式
IF 0.9
Afrika Matematika Pub Date : 2024-04-11 DOI: 10.1007/s13370-024-01183-8
Akbar Ali, Emina Milovanović, Stefan Stankov, Marjan Matejić, Igor Milovanović
{"title":"Inequalities involving the harmonic-arithmetic index","authors":"Akbar Ali,&nbsp;Emina Milovanović,&nbsp;Stefan Stankov,&nbsp;Marjan Matejić,&nbsp;Igor Milovanović","doi":"10.1007/s13370-024-01183-8","DOIUrl":"10.1007/s13370-024-01183-8","url":null,"abstract":"<div><p>Let <i>G</i> be a simple graph with vertex set <span>(V={v_{1},v_{2},ldots ,v_{n}})</span>. The notion <span>(isim j)</span> is used to indicate that the vertices <span>(v_{i})</span> and <span>(v_{j})</span> of <i>G</i> are adjacent. For a vertex <span>(v_{i}in V)</span>, let <span>(d_{i})</span> be the degree of <span>(v_{i})</span>. The harmonic-arithmetic (HA) index of <i>G</i> is defined as <span>(HA(G) =sum _{isim j} 4d_id_j(d_i+d_j)^{-2})</span>. In this paper, a considerable number of inequalities involving the HA index and other topological indices are derived. For every obtained inequality, all the graphs that satisfy the equality case are also characterized.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140713886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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