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Bivariate generalization for operators involving Appostol-Genocchi polynomial 涉及Appostol-Genocchi多项式算子的二元泛化
Annali dell''Universita di Ferrara Pub Date : 2024-12-04 DOI: 10.1007/s11565-024-00562-0
Km. Lipi, Naokant Deo
{"title":"Bivariate generalization for operators involving Appostol-Genocchi polynomial","authors":"Km. Lipi,&nbsp;Naokant Deo","doi":"10.1007/s11565-024-00562-0","DOIUrl":"10.1007/s11565-024-00562-0","url":null,"abstract":"<div><p>This article is primarily concerned with the bivariate generalization of operators involving a class of orthogonal polynomials called Apostol-Genocchi polynomials. The rate of convergence can be determined in terms of partial and total modulus of continuity as well as the order of approximation can be achieved by means of a Lipschitz-type function and Peetre’s K-functional. In addition, we put forth a conceptual extension known as the “generalized boolean sum (GBS)” for these bivariate operators, which aims to establish the degree of approximation for Bögel continuous functions. In this study, we utilize the Mathematica Software to present a series of graphical illustrations that effectively showcase the rate of convergence for the bivariate operators. The graphs indicate that, in the case of certain functions, the bivariate operators exhibits superior convergence when <span>(alpha )</span> is less than <span>(beta )</span>. Based on our analysis and comparison of the error of approximation between the bivariate operators and the corresponding GBS operators, it can be deduced that the GBS operators exhibit a faster convergence towards the function.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761767","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
The parallel postulate 平行公设
Annali dell''Universita di Ferrara Pub Date : 2024-12-03 DOI: 10.1007/s11565-024-00572-y
Victor Pambuccian
{"title":"The parallel postulate","authors":"Victor Pambuccian","doi":"10.1007/s11565-024-00572-y","DOIUrl":"10.1007/s11565-024-00572-y","url":null,"abstract":"<div><p>This is a survey of what is known regarding weaker versions of the Euclidean parallel postulate, culminating with a splitting of the parallel postulate into two weaker and independent incidence-geometric axioms. Among the weaker versions are: the rectangle axiom, stating that there exists a rectangle; the <i>Lotschnittaxiom</i>, stating that the perpendiculars to the sides of a right angle intersect, and Aristotle’s axiom, stating that the distances between the sides of an angle grow indefinitely. Several statements that are equivalent, with plane absolute geometry as a background, to each of these axioms, as well as an analysis of their syntactic simplicity are presented. The parallel postulate is found to be equivalent to the conjunction of the following two axioms: “Given three parallel lines, there is a line that intersects all three of them\" and “Given a line <i>a</i> and a point <i>P</i> on <i>a</i>, as well as two intersecting lines <i>m</i> and <i>n</i>, both parallel to <i>a</i>, there exists a line <i>g</i> through <i>P</i> which intersects <i>m</i> but not <i>n</i>.\"</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761975","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
An inertial method for solving bilevel variational inequality problems with fixed point constraints 求解带不动点约束的二水平变分不等式问题的惯性方法
Annali dell''Universita di Ferrara Pub Date : 2024-11-29 DOI: 10.1007/s11565-024-00571-z
Yirga Abebe Belay, Habtu Zegeye, Oganeditse A. Boikanyo, Dintle Kagiso, Hagos Hailu Gidey
{"title":"An inertial method for solving bilevel variational inequality problems with fixed point constraints","authors":"Yirga Abebe Belay,&nbsp;Habtu Zegeye,&nbsp;Oganeditse A. Boikanyo,&nbsp;Dintle Kagiso,&nbsp;Hagos Hailu Gidey","doi":"10.1007/s11565-024-00571-z","DOIUrl":"10.1007/s11565-024-00571-z","url":null,"abstract":"<div><p>In this paper, we introduce and study an inertial algorithm for solving bilevel variational inequality problems with a fixed point constraint involving a uniformly continuous pseudomonotone mapping in the lower level variational inequality problem and a demimetric mapping for the fixed point constraint. We prove a strong convergence theorem under some suitable conditions on the control sequences. We also provide a numerical example to demonstrate the effectiveness of the method. \u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142754023","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
Spectral analysis of operator matrices: limit point insights 算子矩阵的谱分析：极限点的见解
Annali dell''Universita di Ferrara Pub Date : 2024-11-29 DOI: 10.1007/s11565-024-00573-x
Aymen Bahloul
{"title":"Spectral analysis of operator matrices: limit point insights","authors":"Aymen Bahloul","doi":"10.1007/s11565-024-00573-x","DOIUrl":"10.1007/s11565-024-00573-x","url":null,"abstract":"<div><p>This paper explores the potential of local spectral theory to investigate the limit point set of the descent spectrum of upper triangular operator matrices, denoted by <span>({mathcal {T}})</span>, on Banach spaces. We rigorously prove that transitioning from the accumulation set of the diagonal descent spectrum, denoted by <span>( hbox {Acc} sigma _{textrm{d}}({mathcal {T}}_textbf{diag}))</span>, to that of the complete descent spectrum, <span>( hbox {Acc} sigma _{textrm{d}}({mathcal {T}}))</span>, involves removing specific subsets within <span>( hbox {Acc} sigma _{textrm{d}}(A_1) cap hbox {Acc} sigma _{textrm{a}}(A_2) cap hbox {Acc} sigma _{textrm{a}}(A_3))</span>. Additionally, we present sufficient conditions that ensure the limit points of the descent spectrum of the operator matrix encompass the combined limit points of its diagonal entry spectra. This significantly addresses a longstanding question posed by Campbell (Linear Multilinear Algebra 14:195–198, 1983) regarding the limit points for the descent spectrum of the last <span>(3 times 3)</span> operator matrix form. Specifically, Campbell inquired about developing new methods to analyze the spectral properties of such matrices without resorting to partitioning their entries, a challenge that has remained unresolved for decades. Our findings provide a comprehensive solution, illustrating that a deeper understanding of the spectral behavior can be achieved by considering the entire matrix structure collectively.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753955","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
Location of zeros of quaternionic polynomials 四元多项式的零点位置
Annali dell''Universita di Ferrara Pub Date : 2024-11-22 DOI: 10.1007/s11565-024-00568-8
Idrees Qasim
{"title":"Location of zeros of quaternionic polynomials","authors":"Idrees Qasim","doi":"10.1007/s11565-024-00568-8","DOIUrl":"10.1007/s11565-024-00568-8","url":null,"abstract":"<div><p>In this manuscript, we investigate bounds for the zeros of quaternionic polynomials with restricted coefficients. We find an annular region that contains all the zeros of a quaternionic polynomial. Moreover, we find zero-free regions thereby obtain improvement of Eneström-Kakeya theorem for quaternionic polynomials.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142691874","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
Asymptotic behavior of laminated beams with Kelvin-Voigt damping 具有 Kelvin-Voigt 阻尼的层压梁的渐近行为
Annali dell''Universita di Ferrara Pub Date : 2024-11-21 DOI: 10.1007/s11565-024-00559-9
Victor R. Cabanillas, Teófanes Quispe Méndez
{"title":"Asymptotic behavior of laminated beams with Kelvin-Voigt damping","authors":"Victor R. Cabanillas,&nbsp;Teófanes Quispe Méndez","doi":"10.1007/s11565-024-00559-9","DOIUrl":"10.1007/s11565-024-00559-9","url":null,"abstract":"<div><p>This work considers a one-dimensional system consisting of two identical Timoshenko beams. The model considers that an adhesive layer of small thickness joins the two surfaces, thus producing an interfacial slip under homogeneous mixed Neumann-Dirichlet-Dirichlet boundary conditions. We introduce a Kelvin-Voigt type damping into the rotation equation, and we study the well-posedness of the problem and the asymptotic behavior of the solutions using techniques from the semigroup theory of linear operators and the frequency domain method. When the wave’s propagation speeds are equal in both beams, we show that the Kelvin-Voigt dissipative term acting on the rotation equation is sufficient to obtain the exponential decay of the solutions while maintaining the structural dissipation characteristic of the model. When these propagation speeds differ, we show the lack of exponential decay and prove that the solutions decay polynomially with a decay rate of <span>(t^{-frac{1}{2}})</span>. We prove, finally, that this decay rate is optimal.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679630","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
Borel exceptional values of q-shift polynomials q 移位多项式的 Borel 特殊值
Annali dell''Universita di Ferrara Pub Date : 2024-11-21 DOI: 10.1007/s11565-024-00570-0
M. Tejuswini, N. Shilpa
{"title":"Borel exceptional values of q-shift polynomials","authors":"M. Tejuswini,&nbsp;N. Shilpa","doi":"10.1007/s11565-024-00570-0","DOIUrl":"10.1007/s11565-024-00570-0","url":null,"abstract":"<div><p>This paper deals with the extension of Hayman Conjecture to q-shift differential polynomials generated by meromorphic functions. We prove that the differential polynomials assumes every finite value infinitely often when sharing two Borel exceptional Values with appropriate conditions. Few examples are given to prove that the conditions are inevitable.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679621","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
A class of elliptic system in non reflexive Orlicz-Sobolev spaces 非反射 Orlicz-Sobolev 空间中的一类椭圆系统
Annali dell''Universita di Ferrara Pub Date : 2024-11-20 DOI: 10.1007/s11565-024-00546-0
Hamza El-Houari
{"title":"A class of elliptic system in non reflexive Orlicz-Sobolev spaces","authors":"Hamza El-Houari","doi":"10.1007/s11565-024-00546-0","DOIUrl":"10.1007/s11565-024-00546-0","url":null,"abstract":"<div><p>This paper aims to show that there exists a weak solution to the following quasilinear system driven by the <i>M</i>-Laplacian </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} (-Delta _{m_1})u=F_u(x,u,v)&amp; inquad Omega , (-Delta _{m_2})v=F_v(x,u,v)&amp; inquad Omega , u=v=0&amp; inquad partial Omega , end{array}right. } end{aligned}$$</span></div><div>\u0000 (0.1)\u0000 </div></div><p>where <span>(Omega )</span> is a bounded open subset in <span>({mathbb {R}}^N)</span> and <span>((-Delta _{m}))</span> is the <i>M</i>-Laplacian operator. Here we consider the non-reflexive case taking into account the Orlicz and Orlicz-Sobolev Space. The non-reflexive case occurs when the <i>N</i>-function <span>({overline{M}})</span> does not verify the <span>(Delta _2)</span>-condition. We consider an approximated quasilinear elliptic problem driven by the <span>(M_epsilon )</span>-Laplacian and using the Mountain Pass Theorem to obtain the existence of a nontrivial and nonnegative solution for the above system in reflexive case. By tending <span>(epsilon rightarrow 0)</span> we get the solution in the non-reflexive case.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672417","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
An inertial extragradient algorithm for a common solution of generalized mixed equilibrium problem and fixed point problem of nonexpansive mappings 广义混合均衡问题和非展开映射定点问题共解的惯性外梯度算法
Annali dell''Universita di Ferrara Pub Date : 2024-11-20 DOI: 10.1007/s11565-024-00545-1
Abdellah Bnouhachem
{"title":"An inertial extragradient algorithm for a common solution of generalized mixed equilibrium problem and fixed point problem of nonexpansive mappings","authors":"Abdellah Bnouhachem","doi":"10.1007/s11565-024-00545-1","DOIUrl":"10.1007/s11565-024-00545-1","url":null,"abstract":"<div><p>In this paper, we propose an inertial iterative method for approximating a common solution of generalized mixed equilibrium problem for monotone and uniformly continuous operators and fixed point of nonexpansive mapping in real Hilbert space. The strong convergence of the sequence generated by the proposed method can be guaranteed without prior knowledge of the Lipschitz constant of the operator. Preliminary numerical experiments are included to verify the theoretical assertions of the proposed method. Our result improves, extends and generalizes several of the existing results in this direction.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672451","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
A generalization of singular modules in terms of purely extending property 从纯扩展性质看奇异模块的一般化
Annali dell''Universita di Ferrara Pub Date : 2024-11-14 DOI: 10.1007/s11565-024-00567-9
Enas Mustafa Kamil, Bijan Davvaz
{"title":"A generalization of singular modules in terms of purely extending property","authors":"Enas Mustafa Kamil,&nbsp;Bijan Davvaz","doi":"10.1007/s11565-024-00567-9","DOIUrl":"10.1007/s11565-024-00567-9","url":null,"abstract":"<div><p>In this article, we present and examine a type of modules that represent appropriate generalizations of each of the singular modules, purely extending and CCLS modules. A module <i>M</i> is called purely CCLS module if every c-closed submodule of <i>M</i> is pure in <i>M</i>. We locate purely CCLS module with generalizations of extending modules. We present some characterizations of purely CCLS and we show that the direct summand of purely CCLS modules is again purely CCLS. Furthermore, we go over when a direct sum of purely CCLS is likewise purely CCLS. Additionally, we provide adequate circumstances under which the direct sum of purely CCLS is purely CCLS.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636665","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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