Afrika Matematika最新文献_第8页

New improvements of some classical inequalities 一些经典不等式的新改进

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Afrika Matematika Pub Date : 2024-11-26 DOI: 10.1007/s13370-024-01218-0

Abdelmajid Gourty, Mohamed Amine Ighachane, Fuad Kittaneh

{"title":"New improvements of some classical inequalities","authors":"Abdelmajid Gourty, Mohamed Amine Ighachane, Fuad Kittaneh","doi":"10.1007/s13370-024-01218-0","DOIUrl":"10.1007/s13370-024-01218-0","url":null,"abstract":"<div><p>In this paper, we establish an inequality for scalars, which we then apply to refine some classical inequalities for inner product and numerical raduis. For example, we establish that for any <span>(mathcal {E}in mathcal {B}(mathcal {H}),)</span> <span>(u,vin mathcal {H},)</span> and <span>(0le theta le 1)</span>, </p><div><div><span>$$begin{aligned} |langle mathcal {E} u,vrangle |^2&le mathcal {U}_{(n,xi )}left( eta ,|langle mathcal {E}u,vrangle |,sqrt{leftlangle |mathcal {E}|^{2 theta } u,urightrangle leftlangle left| mathcal {E}^*right| ^{2(1-theta )} v, vrightrangle }right) &le leftlangle |mathcal {E}|^{2 theta } u,urightrangle leftlangle left| mathcal {E}^*right| ^{2(1-theta )} v, vrightrangle . end{aligned}$$</span></div></div><p>Moreover, we have <span>(left( mathcal {U}_{(n,xi )}left( eta ,|langle mathcal {E}u,vrangle |,sqrt{leftlangle |mathcal {E}|^{2 theta } u,urightrangle leftlangle left| mathcal {E}^*right| ^{2(1-theta )} v, vrightrangle }right) right) _{n geqslant 0})</span> is an increasing sequence satisfying </p><div><div><span>$$begin{aligned} lim limits _{n rightarrow +infty } mathcal {U}_{(n,xi )}left( eta ,|langle mathcal {E}u,vrangle |,sqrt{leftlangle |mathcal {E}|^{2 theta } u,urightrangle leftlangle left| mathcal {E}^*right| ^{2(1-theta )} v, vrightrangle }right) = leftlangle |mathcal {E}|^{2 theta } u,urightrangle leftlangle left| mathcal {E}^*right| ^{2(1-theta )} v, vrightrangle , end{aligned}$$</span></div></div><p>which presents a novel refinement of the well-known mixed Schwartz inequality. Our results extend and refine well-established inequalities found in the literature.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714503","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 Bazilevi(breve{c}) type univalent class defined through subordination 通过从属关系定义的 Bazilevi（breve{c}）型单价类的某些性质

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Afrika Matematika Pub Date : 2024-10-10 DOI: 10.1007/s13370-024-01216-2

T. Panigrahi, S. Jena, R. M. El-Ashwah

引用次数: 0

Characterizations of (mathcal{Q}mathcal{C})-hyperideals in semihypergroups 半超群中的(mathcal{Q}mathcal{C})-超次数的特征

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Afrika Matematika Pub Date : 2024-09-27 DOI: 10.1007/s13370-024-01215-3

Shahnawaz Ali, Mohammad Y. Abbasi, Kostaq Hila, Sabahat A. Khan

引用次数: 0

The Diophantine equation (T_l=mathcal {U}_n -mathcal {U}_m) Diophantine equation （T_l=mathcal {U}_n -mathcal {U}_m)

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Afrika Matematika Pub Date : 2024-09-21 DOI: 10.1007/s13370-024-01214-4

Pagdame Tiebekabe, Kossi Richmond Kakanou, Ismaïla Diouf

引用次数: 0

A numerical block hybrid algorithm for solving systems of first-order initial value problems 求解一阶初值问题系统的数值块混合算法

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Afrika Matematika Pub Date : 2024-09-06 DOI: 10.1007/s13370-024-01213-5

Nathaniel Mahwash Kamoh, Bwebum Cleofas Dang, Joshua Sunday

{"title":"A numerical block hybrid algorithm for solving systems of first-order initial value problems","authors":"Nathaniel Mahwash Kamoh, Bwebum Cleofas Dang, Joshua Sunday","doi":"10.1007/s13370-024-01213-5","DOIUrl":"10.1007/s13370-024-01213-5","url":null,"abstract":"<div><p>Attracted by the importance of ordinary differential equations in many physical situations like, engineering, business and health care in particular, an effective and successful numerical algorithm is needed in order to explain many of the ambiguities about the phenomena in many fields of human endeavor. In this study, an interpolation and collocation technique are adopted in deriving a Block Hybrid Algorithm (BHA) for the numerical solution of systems of first-order Initial Value Problems (IVPs). To derive the BHA, the shifted Legendre polynomials was interpolated at two selected points and its derivative was collocated at seven selected points. This led to a continuous scheme which was eventually evaluated at some points to obtain the discrete schemes used in the numerical computation. Furthermore, some illustrative examples are introduced to show the applicability and validity of the proposed algorithm. It was observed that the proposed algorithm has the desired rate of convergence to the exact solution. The suggested method utilizes data at points other than the step numbers which is viewed as an important landmark; another major advantage of this algorithm is that it possesses remarkably small error constants (Table 2). Some graphical representations of the exact and numerical results are presented to show how accurate the numerical results agree with the exact solutions.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-024-01213-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410283","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

Local existence and blow up for the wave equation with nonlinear logarithmic source term and nonlinear dynamical boundary conditions combined with distributed delay 带有非线性对数源项和非线性动力学边界条件的波方程的局部存在性和炸毁，以及分布式延迟

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Afrika Matematika Pub Date : 2024-08-24 DOI: 10.1007/s13370-024-01212-6

Abdelbaki Choucha, Salah Boulaaras, Mohammad Alnegga

引用次数: 0

Multilevel wavelet packets in sobolev space over local fields of positive characteristic 在正特征局部域上的索波列夫空间中的多级小波包

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Afrika Matematika Pub Date : 2024-08-17 DOI: 10.1007/s13370-024-01211-7

Ashish Pathak, Guru P. Singh

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Perov type T-contractive mappings on cone b-metric spaces with generalized c-distance 具有广义c-距离的锥体b-度量空间上的佩罗夫型T-收缩映射

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Afrika Matematika Pub Date : 2024-08-14 DOI: 10.1007/s13370-024-01210-8

Talat Nazir, Mujahid Abbas, Sergei Silvestrov

引用次数: 0

Development of a Fourier–Stieltjes transform using an induced representation on locally compact groups 利用局部紧凑群上的诱导表示发展傅立叶-斯蒂尔杰斯变换

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Afrika Matematika Pub Date : 2024-08-12 DOI: 10.1007/s13370-024-01199-0

Yao Ihébami Akakpo, Mahouton Norbert Hounkonnou, Koffi Enakoutsa, Kofi V. S. Assiamoua

{"title":"Development of a Fourier–Stieltjes transform using an induced representation on locally compact groups","authors":"Yao Ihébami Akakpo, Mahouton Norbert Hounkonnou, Koffi Enakoutsa, Kofi V. S. Assiamoua","doi":"10.1007/s13370-024-01199-0","DOIUrl":"10.1007/s13370-024-01199-0","url":null,"abstract":"<div><p>In our research, we broaden the scope of Fourier–Stieltjes transforms to encompass locally compact groups, denoted as <i>G</i>. We achieve this extension by leveraging the induced representation from a closed subgroup <i>K</i>. From this, we deduce the Fourier transform <span>({hat{f}})</span> of a Haar-integrable function <i>f</i> defined on <i>G</i>. Specifically, we express <span>({hat{f}})</span> as the Fourier–Stieltjes transform <span>({hat{mu }})</span> of the measure <span>(mu = f lambda )</span>, where <span>( lambda )</span> denotes the Haar measure of <i>G</i>. Our work is significant because when applied to Lie groups with compact subgroups <i>K</i>, our Fourier–Stieltjes transform <span>({hat{m}})</span> exhibits more nuanced characteristics compared to the traditionally defined one via the Gel’fand transform, which is standard in the context of Lie groups. We rigorously substantiate this observation. One of the principal challenges we confront is the construction of the “trigonometric functions”, which serve as the foundation for building the Fourier transform.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411425","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 Cayley sum signed graphs-II 关于 Cayley 和符号图-II

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Afrika Matematika Pub Date : 2024-08-05 DOI: 10.1007/s13370-024-01209-1

Deepakshi Sharma, Sachin Somra, Deepa Sinha

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