Afrika MatematikaPub Date : 2024-08-12DOI: 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}
Afrika MatematikaPub Date : 2024-08-05DOI: 10.1007/s13370-024-01209-1
Deepakshi Sharma, Sachin Somra, Deepa Sinha
{"title":"On Cayley sum signed graphs-II","authors":"Deepakshi Sharma, Sachin Somra, Deepa Sinha","doi":"10.1007/s13370-024-01209-1","DOIUrl":"10.1007/s13370-024-01209-1","url":null,"abstract":"<div><p>The Cayley sum graph is a graph whose vertex comprises elements of an abelian group <i>G</i> and edges are the sum of these vertices belonging to a subset of <i>G</i>, namely, <i>S</i>. We introduce Cayley sum signed graph by giving the sign to these edges. An edge receives a positive sign if any of the incident vertices belong to <i>S</i>; otherwise, it receives a negative sign. We discuss the balance, clusterability and some properties of derived Cayley sum signed graph.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409975","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}
{"title":"A modified Thakur’s iteration for noncyclic Suzuki’s relatively nonexpansive mappings with convergence of best proximity pairs","authors":"Sangkhae Suwansoontorn, Nawitcha Onjai-Uea, Thanyarat Jitpeera, Chirasak Mongkolkeha, Konrawut Khammahawong","doi":"10.1007/s13370-024-01206-4","DOIUrl":"10.1007/s13370-024-01206-4","url":null,"abstract":"<div><p>In this paper, we modify the Thakur three-step iterative algorithm and provide sufficient conditions and a useful lemma to ensure the convergence of a best proximity pair for a noncyclic relatively Suzuki’s nonexpansive mapping in uniformly convex Banach spaces. Additionally, we present an example to illustrate the results, accompanied by a numerical simulation for the proposed algorithm.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415363","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}
Afrika MatematikaPub Date : 2024-07-27DOI: 10.1007/s13370-024-01203-7
Sachin Somra, Deepakshi Sharma, Deepa Sinha
{"title":"On Cayley sum signed graphs-I","authors":"Sachin Somra, Deepakshi Sharma, Deepa Sinha","doi":"10.1007/s13370-024-01203-7","DOIUrl":"10.1007/s13370-024-01203-7","url":null,"abstract":"<div><p>The Cayley sum graph is a graph whose vertex comprises elements of an abelian group <i>G</i>, and edges are the sum of these vertices belonging to a subset of <i>G</i>, namely, <i>S</i>. We introduce the Cayley sum signed graph by giving the sign to these edges. An edge receives a positive sign if any of the incident vertices belong to <i>S</i>. Otherwise, it receives a negative sign. We discuss the properties of the Cayley sum signed graph.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141797912","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}
Afrika MatematikaPub Date : 2024-07-26DOI: 10.1007/s13370-024-01204-6
Mojtaba Sedaghatjoo, Roghaieh Khosravi, Mohammad Roueentan
{"title":"Principal right congruences on completely 0-simple semigroups","authors":"Mojtaba Sedaghatjoo, Roghaieh Khosravi, Mohammad Roueentan","doi":"10.1007/s13370-024-01204-6","DOIUrl":"10.1007/s13370-024-01204-6","url":null,"abstract":"<div><p>In this paper principal right congruences on completely 0-simple semigroups are identified which consequently leads to identifying principal right congruences on classes of semigroups namely, Brandt semigroups, right groups, left groups, right zero semigroups, left zero semigroups and rectangular bands. As a consequence of this characterization, we show that the class of right subdirectly irreducible completely 0-simple semigroups with more than 3 elements is that of cocyclic 0-groups. Moreover, we prove that right irreducible completely 0-simple semigroups with more than 3 elements are 0-groups for which nontrivial subgroups have nontrivial intersections.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141799555","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}
Afrika MatematikaPub Date : 2024-07-26DOI: 10.1007/s13370-024-01205-5
Bilender P. Allahverdiev, Hüseyin Tuna, Hamlet A. Isayev
{"title":"The resolvent of impulsive dynamic singular Sturm–Liouville operators","authors":"Bilender P. Allahverdiev, Hüseyin Tuna, Hamlet A. Isayev","doi":"10.1007/s13370-024-01205-5","DOIUrl":"10.1007/s13370-024-01205-5","url":null,"abstract":"<div><p>In this study, the resolvent operator of the impulsive dynamic singular Sturm–Liouville problem is considered. The spectral function was first established. The integral representation of the resolvent operator is obtained using this function.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141798978","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}
Afrika MatematikaPub Date : 2024-07-26DOI: 10.1007/s13370-024-01208-2
Tijani A. Apalara, Salim A. Messaoud, Mostafa Zahri
{"title":"Asymptotic stability of porous-elasticity with microtemparature of second-sound type","authors":"Tijani A. Apalara, Salim A. Messaoud, Mostafa Zahri","doi":"10.1007/s13370-024-01208-2","DOIUrl":"10.1007/s13370-024-01208-2","url":null,"abstract":"<div><p>In this work, we establish exponential and polynomial decay results for a one-dimensional porous-elastic system with microtemperatures depending on the system’s parameters. Our results are new and improve some previous literature results where additional damping terms were required to establish the exponential decay result. We also present some numerical tests to illustrate our theoretical results.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141799598","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}
Afrika MatematikaPub Date : 2024-07-25DOI: 10.1007/s13370-024-01207-3
Amine Marah
{"title":"Existence and uniqueness results for an elliptic equation with blowing-up coefficient and lower order term","authors":"Amine Marah","doi":"10.1007/s13370-024-01207-3","DOIUrl":"10.1007/s13370-024-01207-3","url":null,"abstract":"<div><p>This paper deals with the existence and uniqueness results for a class of non-coercive Dirichlet elliptic problems whose model example is </p><div><div><span>$$begin{aligned} left{ begin{aligned}&-textrm{div}Big (frac{1}{(m-u)^beta } (1+|u|)^q |nabla u|^{p-2}nabla u+c(x)|u|^{p-2}u sin (u-m)Big )+g(u)=f textrm{in} Omega , &u=0 textrm{on} {partial Omega }, end{aligned} right. end{aligned}$$</span></div></div><p>where <span>(Omega )</span> is a bounded open subset of <span>({mathbb {R}}^N (Nge 2))</span>, <span>(1< p < N)</span>, <span>(m>0)</span>, <span>(0< beta <1)</span>, <span>(q>0)</span>, |<i>c</i>| belongs to <span>(L^{frac{N}{p-1}}(Omega ))</span> and <i>g</i> is a continuous function in <span>({mathbb {R}})</span> which satisfies the sign condition and the data <i>f</i> belongs to <span>(L^1(Omega ))</span>.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141802340","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}
Afrika MatematikaPub Date : 2024-07-21DOI: 10.1007/s13370-024-01201-9
Lai Van Phut
{"title":"Finite-time stability analysis of fractional fuzzy differential equations with time-varying delay involving the generalized Caputo fractional derivative","authors":"Lai Van Phut","doi":"10.1007/s13370-024-01201-9","DOIUrl":"10.1007/s13370-024-01201-9","url":null,"abstract":"<div><p>The main results of this paper are to discuss the primary results of fuzzy differential equations with time-varying delay (FDDEs) via the generalized Caputo fractional derivative. We establish the existence of a unique solution for FDDEs using the method of steps and the generalized Gronwall inequality. Sufficient conditions are proposed to ensure the finite-time stability (FTS) of FDDEs. Finally, we explore specific examples to illustrate and reinforce the results obtained.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141818712","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}
Afrika MatematikaPub Date : 2024-07-15DOI: 10.1007/s13370-024-01202-8
Somayeh Borhani Nejad Rayeni, Bijan Davvaz
{"title":"On enumeration of hyper nearrings of order less than 4 and their automorphisms","authors":"Somayeh Borhani Nejad Rayeni, Bijan Davvaz","doi":"10.1007/s13370-024-01202-8","DOIUrl":"10.1007/s13370-024-01202-8","url":null,"abstract":"<div><p>In this paper, we partition, enumerate and classify hyper nearrings up to isomorphism of order less than 4 and then determine their automorphism groups.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141645284","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}