In this article, we examine the stability of first-order linear quaternion-valued differential equations using the Mittag-Leffler-Hyers-Ulam approach. We achieve this by transforming a linear quaternion-valued differential equation into a real differential system. The stability outcomes for these linear quaternion-valued differential equations are determined through the use of quaternion module and Fourier transform techniques.
{"title":"Stability analysis of linear quaternion-valued differential equation using integral transform","authors":"A. Mohanapriya","doi":"10.56947/amcs.v22.274","DOIUrl":"https://doi.org/10.56947/amcs.v22.274","url":null,"abstract":"In this article, we examine the stability of first-order linear quaternion-valued differential equations using the Mittag-Leffler-Hyers-Ulam approach. We achieve this by transforming a linear quaternion-valued differential equation into a real differential system. The stability outcomes for these linear quaternion-valued differential equations are determined through the use of quaternion module and Fourier transform techniques.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"115 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140370725","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}
The present study deals with asymptotically equivalent sequences in partial metric spaces. We define the notions of strongly asymptotically lacunary equivalence, asymptotically statistical equivalence, and asymptotically lacunary statistical equivalence. We theoretically contribute to these notions and investigate some of their basic properties.
{"title":"Asymptotically Lacunary statistical equivalent sequences in partial metric spaces","authors":"Ahmet Çaki, Aykut Or","doi":"10.56947/amcs.v22.262","DOIUrl":"https://doi.org/10.56947/amcs.v22.262","url":null,"abstract":"The present study deals with asymptotically equivalent sequences in partial metric spaces. We define the notions of strongly asymptotically lacunary equivalence, asymptotically statistical equivalence, and asymptotically lacunary statistical equivalence. We theoretically contribute to these notions and investigate some of their basic properties.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"33 31","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140372567","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}
If p(z) is a polynomial of degree n having no zero in |z|1, then Govil and Rahman [10] extended Malik's inequality [13] into Lr version. In this paper, we prove improved and generalized versions of the above inequality.
如果 p(z) 是 |z|1 中没有零点的 n 阶多项式，那么 Govil 和 Rahman [10] 将 Malik 不等式 [13] 扩展为 Lr 版本。本文将证明上述不等式的改进版和广义版。
{"title":"L^r inequalities for polynomials with restricted zeros","authors":"Singhajit Mayanglambam, M. S. Singh, B. Chanam","doi":"10.56947/amcs.v21.258","DOIUrl":"https://doi.org/10.56947/amcs.v21.258","url":null,"abstract":"If p(z) is a polynomial of degree n having no zero in |z|1, then Govil and Rahman [10] extended Malik's inequality [13] into Lr version. In this paper, we prove improved and generalized versions of the above inequality.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"52 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139960272","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}
The object of the paper is to investigate invariant submanifolds of an almost alpha-cosymplectic (k, mu, nu )-space. Then we have proved that the necessary and sufficient conditions for an invariant submanifold of an almost alpha-cosymplectic (k, mu, nu )-space to be totally geodesic under the some conditions. Consequently, we have obtained some interesting results invariant submanifolds of an almost alpha-cosymplectic (k, mu, nu )-space.
本文的目的是研究几乎阿尔法余弦（k, mu, nu ）空间的不变子曼形体。首先，我们证明了几乎α-余弦（k, mu, nu ）空间的不变子曼形体在某些条件下是完全测地的必要条件和充分条件；然后，我们证明了几乎α-余弦（k, mu, nu ）空间的不变子曼形体在某些条件下是完全测地的必要条件和充分条件。因此，我们得到了一些有趣的几乎阿尔法余弦（k, mu, nu ）空间的不变子曼形体的结果。
{"title":"Some important properties of invariant submanifolds of an almost alpha-cosymplectic (k, mu, nu )-space","authors":"Pakize Uygun, M. Atc̣eken, Tuğba Mert","doi":"10.56947/amcs.v21.242","DOIUrl":"https://doi.org/10.56947/amcs.v21.242","url":null,"abstract":"The object of the paper is to investigate invariant submanifolds of an almost alpha-cosymplectic (k, mu, nu )-space. Then we have proved that the necessary and sufficient conditions for an invariant submanifold of an almost alpha-cosymplectic (k, mu, nu )-space to be totally geodesic under the some conditions. Consequently, we have obtained some interesting results invariant submanifolds of an almost alpha-cosymplectic (k, mu, nu )-space.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"62 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139960380","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}
The paper discusses the existence of entire solutions for k th derivative of certain type of non-linear differential-difference equations. In addition to, the paper evaluates some previous results for existence of finite order transcendental entiresolutions and extends to the higher order. Particularly, we obtain the conditions for occurrence and attainable forms of entire solutions.
{"title":"Existence of entire solutions for k-th derivative of certain type of non-linear differential-difference equations","authors":"Jayashri Pattar, Shilpa N","doi":"10.56947/amcs.v21.250","DOIUrl":"https://doi.org/10.56947/amcs.v21.250","url":null,"abstract":"The paper discusses the existence of entire solutions for k th derivative of certain type of non-linear differential-difference equations. In addition to, the paper evaluates some previous results for existence of finite order transcendental entiresolutions and extends to the higher order. Particularly, we obtain the conditions for occurrence and attainable forms of entire solutions.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"59 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139960580","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}
To solve the Newell-White-Segel equations (NWSE), this paper presents a novel analytical method that combines the Mohand Transform with the HPM in a unique way. Due to its intrinsic nonlinearity, NWSE, which is essential for simulating intricate events in mathematical biology and physics, poses analytical challenges. An efficient analytical framework for dealing with nonlinear systems is provided by extending the Mohand Transform in combination with the HPM. Comparative evaluations between the results of this study and those of previous research, together with proven analytical solutions, are carried out in the framework of three NWSE examples.
{"title":"Application of Mohand transform coupled with homotopy perturbation method to solve Newel-White-Segel equation","authors":"Olubanwo Oludapo Omotola, Adepoju Julius Temiatyo, Ajani Abiodun Sufiat, Shobowale Abiodun Ezekiel","doi":"10.56947/amcs.v21.267","DOIUrl":"https://doi.org/10.56947/amcs.v21.267","url":null,"abstract":"To solve the Newell-White-Segel equations (NWSE), this paper presents a novel analytical method that combines the Mohand Transform with the HPM in a unique way. Due to its intrinsic nonlinearity, NWSE, which is essential for simulating intricate events in mathematical biology and physics, poses analytical challenges. An efficient analytical framework for dealing with nonlinear systems is provided by extending the Mohand Transform in combination with the HPM. Comparative evaluations between the results of this study and those of previous research, together with proven analytical solutions, are carried out in the framework of three NWSE examples.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"85 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139959639","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}
We consider some sequential conditions for the convolvability of two ultradistributions, specifically the Roumieu ultradistributions defined on the space of all ultradifferentiable functions Dn{M_p} in the space Dn'{M_p} and show the similarities between these conditions in the sense of Mincheva-Kaminska S. The sequential conditions are based on the use of approximate identities which satisfy certain conditions to be a Banach algebra for the space Dn{M_p} . We present an equivalent result involving the convolution of the differentiability of two Roumieu ultradistributions with equivalent norm condition.
我们考虑了两个超分布的可卷积性的一些顺序条件，特别是定义在空间 Dn'{M_p} 中所有超微分函数空间 Dn{M_p} 上的 Roumieu 超分布，并展示了这些条件在 Mincheva-Kaminska S 意义上的相似性。我们提出了一个等价结果，涉及两个具有等价规范条件的鲁米厄超分布的可微分性的卷积。
{"title":"Some results on ultradifferential convolution property of ultradistributions","authors":"Anslem Amaonyeiro, K. Isife","doi":"10.56947/amcs.v21.264","DOIUrl":"https://doi.org/10.56947/amcs.v21.264","url":null,"abstract":"We consider some sequential conditions for the convolvability of two ultradistributions, specifically the Roumieu ultradistributions defined on the space of all ultradifferentiable functions Dn{M_p} in the space Dn'{M_p} and show the similarities between these conditions in the sense of Mincheva-Kaminska S. The sequential conditions are based on the use of approximate identities which satisfy certain conditions to be a Banach algebra for the space Dn{M_p} . We present an equivalent result involving the convolution of the differentiability of two Roumieu ultradistributions with equivalent norm condition. \u0000 ","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"69 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139960138","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}
In this work, we study the convergence of a sequence of solutions of degener- ate elliptic problems with variable coercivity and growth exponents. The functional setting involves Lebesgue and Sobolev spaces with variable exponent which varies also with n.
在这项工作中，我们研究了具有可变矫顽力和增长指数的退化椭圆问题解序列的收敛性。函数设置涉及具有可变指数的 Lebesgue 和 Sobolev 空间，指数也随 n 变化。
{"title":"Structural stability of p(x)-Laplacian kind problems with maximal monotone graphs and Neumann type boundary condition","authors":"S. Ouaro, Kpê Kansié","doi":"10.56947/amcs.v21.247","DOIUrl":"https://doi.org/10.56947/amcs.v21.247","url":null,"abstract":"\u0000 \u0000 \u0000In this work, we study the convergence of a sequence of solutions of degener- ate elliptic problems with variable coercivity and growth exponents. The functional setting involves Lebesgue and Sobolev spaces with variable exponent which varies also with n. \u0000 \u0000 \u0000","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"63 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139959900","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}
The purpose of this article, is to establish some fixed point results for fuzzy mappings in a complete dislocated b-metric space. Examples are provided to support results and concepts presented herein. As an application of our results, multivalued mappings and fuzzy mappings are studied.
{"title":"Fixed point theorems for fuzzy contractions mappings in a dislocated b-metric spaces with applications","authors":"Muhammed Raji, Musa Adeku Ibrahim","doi":"10.56947/amcs.v21.233","DOIUrl":"https://doi.org/10.56947/amcs.v21.233","url":null,"abstract":"The purpose of this article, is to establish some fixed point results for fuzzy mappings in a complete dislocated b-metric space. Examples are provided to support results and concepts presented herein. As an application of our results, multivalued mappings and fuzzy mappings are studied.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"85 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139959481","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}
Motivated by the results previously reported, the current work aims at developing new numerical radius upper bounds of Hilbert space opera- tors by offering new improvements to the well-known Cauchy-Schwarz inequal- ity. In particular, a novel Lemma (3.1) is given, which is utilized to further generalize several vector and numerical radius type inequalities, as well as pre- viously given extensions of the Cauchy-Schwartz inequality. Specifically, (2.5) (2.8) (1.6) have been generalized by (4.3) (4.1) (4.2)
{"title":"Refinement of the Cauchy-Schwartz inequality with refinements and generalizations of the numerical radius type inequalities for operators","authors":"Vuk Stojiljković, S. Dragomir","doi":"10.56947/amcs.v21.246","DOIUrl":"https://doi.org/10.56947/amcs.v21.246","url":null,"abstract":"\u0000\u0000\u0000Motivated by the results previously reported, the current work aims at developing new numerical radius upper bounds of Hilbert space opera- tors by offering new improvements to the well-known Cauchy-Schwarz inequal- ity. In particular, a novel Lemma (3.1) is given, which is utilized to further generalize several vector and numerical radius type inequalities, as well as pre- viously given extensions of the Cauchy-Schwartz inequality. Specifically, (2.5) (2.8) (1.6) have been generalized by (4.3) (4.1) (4.2)\u0000\u0000\u0000","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"63 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139959901","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}
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