Afrika MatematikaPub Date : 2023-11-10DOI: 10.1007/s13370-023-01127-8
Priyanka Chhaparwal, Sanjay Kumar
{"title":"Robust ratio and product based estimators using known auxiliary information through modified maximum likelihood","authors":"Priyanka Chhaparwal, Sanjay Kumar","doi":"10.1007/s13370-023-01127-8","DOIUrl":"10.1007/s13370-023-01127-8","url":null,"abstract":"<div><p>In this paper, we consider the situation where the underlying distribution of the study variable is not normally distributed. Under such situations, we propose ratio and product based estimators for the finite population mean in simple random sampling using known auxiliary information based on order statistics. We obtain the expressions for biases and mean square errors (MSEs) of the proposed estimators, which show that the proposed estimators have less MSEs and biases than other existing estimators. Simulations have been studied under various super-population models. A real life application is also provided. Robustness properties of the proposed estimators have been studied via simulations. Confidence intervals (CIs) show that the proposed estimators have shorter CIs of estimates than those of the existing estimators.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"34 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795973","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":"Global nonexistence of solution for a nonlinear Klein–Gordon equation with strong damping, distributed delay and source terms","authors":"Fares Yazid, Djamel Ouchenane, Fatima Siham Djeradi, Rafik Guefaifia","doi":"10.1007/s13370-023-01137-6","DOIUrl":"10.1007/s13370-023-01137-6","url":null,"abstract":"<div><p>In the present work, we consider a nonlinear Klein–Gordon equation with strong damping, distributed delay and source terms. Under suitable conditions, we prove the blow-up result of solutions. Our result is an extension of many other works in this area.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"34 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795971","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 : 2023-11-09DOI: 10.1007/s13370-023-01135-8
S. Sohrabi
{"title":"Wavelets direct method for solving volterra integral-algebraic equations","authors":"S. Sohrabi","doi":"10.1007/s13370-023-01135-8","DOIUrl":"10.1007/s13370-023-01135-8","url":null,"abstract":"<div><p>This paper deals with the numerical solutions for Volterra type integral-algebraic equations (IAEs) via a direct method using Legendre wavelets (LWs). Using the operational matrix associated with Legendre wavelets the problem is transformed to a linear system of algebraic equations. This approach does not use any variable transformations, so all calculations can be easily implemented. Convergence rate and numerical examples are presented to illustrate the efficiency and applicability of the method.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"34 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795729","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 : 2023-11-08DOI: 10.1007/s13370-023-01131-y
Takao Komatsu, Rusen Li
{"title":"Summation formulas of hyperharmonic numbers with their generalizations","authors":"Takao Komatsu, Rusen Li","doi":"10.1007/s13370-023-01131-y","DOIUrl":"10.1007/s13370-023-01131-y","url":null,"abstract":"<div><p>In 1990, Spieß gave some identities of harmonic numbers including the types <span>(sum _{ell =1}^nell ^k H_ell )</span>, <span>(sum _{ell =1}^nell ^k H_{n-ell })</span> and <span>(sum _{ell =1}^nell ^k H_ell H_{n-ell })</span>. In this paper, we derive several formulas of hyperharmonic numbers including <span>(sum _{ell =0}^{n} {ell }^{p} h_{ell }^{(r)} h_{n-ell }^{(s)})</span> and <span>(sum _{ell =0}^n ell ^{p}left( h_{ell }^{(r)}right) ^{2})</span>. Some more formulas of generalized hyperharmonic numbers are also shown.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"34 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878273","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 : 2023-11-02DOI: 10.1007/s13370-023-01124-x
M. El Hamma, R. Daher, A. Mahfoud, H. Lahmadi
{"title":"Some inequalities involving Fourier transforms","authors":"M. El Hamma, R. Daher, A. Mahfoud, H. Lahmadi","doi":"10.1007/s13370-023-01124-x","DOIUrl":"10.1007/s13370-023-01124-x","url":null,"abstract":"<div><p>We obtain new inequalities for the Fourier transform in the space <span>(textrm{L}^{p}(mathbb {R}^{n}))</span>, <span>(1<ple 2)</span>, using a generalized spherical mean operator for proving the estimates in certain classes of functions characterized by a generalized continuity modulus.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"34 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-023-01124-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878222","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}
Afrika MatematikaPub Date : 2023-11-02DOI: 10.1007/s13370-023-01121-0
Ho Vu
{"title":"On the Caputo fractional random boundary value problem","authors":"Ho Vu","doi":"10.1007/s13370-023-01121-0","DOIUrl":"10.1007/s13370-023-01121-0","url":null,"abstract":"<div><p>In this paper, we aim to prove the existence and uniqueness of the mean square solution to the Caputo fractional random boundary value problem by using the fixed point theorems. Moreover, we introduce the Ulam–Hyers stability and generalized Ulam–Hyers stability for this problem. Finally, we give an example to illustrate our results.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"34 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878223","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 : 2023-11-01DOI: 10.1007/s13370-023-01125-w
Young Bae Jun, Seok-Zun Song, Eun Hwan Roh
{"title":"Soju structures with applications in BCK/BCI-algebras","authors":"Young Bae Jun, Seok-Zun Song, Eun Hwan Roh","doi":"10.1007/s13370-023-01125-w","DOIUrl":"10.1007/s13370-023-01125-w","url":null,"abstract":"<div><p>A new structure, so called soju structure, is introduced by combining intuitionistic fuzzy set and soft set, which is applied to <i>BCK</i>/<i>BCI</i>-algebras. The notions of soju subalgebra and soju ideal in <i>BCK</i>/<i>BCI</i>-algebras are introduced, and related properties are investigated. A strong soju subalgebra in <i>BCI</i>-algebras is introduced, and a condition for a soju subalgebra to be strong is provided. Relations between soju subalgebra and soju ideal are discussed, and conditions for a soju structure to be a soju ideal in a <i>BCK</i>-algebra are considered. Characterizations of soju subalgebra and soju ideal are considered, and the homomorphic image and preimage of soju subalgebra is discussed.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"34 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795353","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 : 2023-10-30DOI: 10.1007/s13370-023-01110-3
K. Dhilip Kumar, M. Ramachandran
{"title":"Near rings characterized by intuitionistic fuzzy weak bi ideals","authors":"K. Dhilip Kumar, M. Ramachandran","doi":"10.1007/s13370-023-01110-3","DOIUrl":"10.1007/s13370-023-01110-3","url":null,"abstract":"<div><p>Generalizing the idea of fuzzy weak bi ideals of near ring, the notion of intuitionistic fuzzy weak bi ideals of near ring is defined. Specially, we obtain a characterization of near ring in terms of intuitionistic fuzzy weak bi ideals.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"34 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797945","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 : 2023-10-28DOI: 10.1007/s13370-023-01119-8
Sangeeta Saha, Binod Chandra Tripathy
{"title":"Statistical Fibonacci convergence of complex uncertain variables","authors":"Sangeeta Saha, Binod Chandra Tripathy","doi":"10.1007/s13370-023-01119-8","DOIUrl":"10.1007/s13370-023-01119-8","url":null,"abstract":"<div><p>This paper presents several statistical convergence concepts of complex uncertain sequences based on a regular matrix of Fibonacci numbers: statistical Fibonacci convergence almost surely, statistical Fibonacci convergence in measure, statistical Fibonacci convergence in mean and statistical Fibonacci convergence uniformly almost surely. Furthermore, the interrelations between them are studied and depicted in the form of a diagram.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"34 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797563","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 : 2023-10-27DOI: 10.1007/s13370-023-01117-w
El Houcine Rami, Elhoussine Azroul, Abdelkrim Barbara
{"title":"Existence of solutions for some quasilinear elliptic system with weight and measure-valued right hand side","authors":"El Houcine Rami, Elhoussine Azroul, Abdelkrim Barbara","doi":"10.1007/s13370-023-01117-w","DOIUrl":"10.1007/s13370-023-01117-w","url":null,"abstract":"<div><p>Let <span>(Omega )</span> be an open bounded domain in <span>(I!!R^{n},)</span> we prove the existence of a solution <i>u</i> for the nonlinear elliptic system </p><div><div><span>$$begin{aligned} text{(QES) } left{ begin{array}{ll} -divsigma left( x,uleft( xright) ,Duleft( xright) right) = mu &{}quad text{ in } Omega u = 0 &{}quad text{ on } partial Omega , end{array} right. end{aligned}$$</span></div><div>\u0000 (0.1)\u0000 </div></div><p>where <span>(mu )</span> is Radon measure on <span>(Omega )</span> with finite mass. In particular, we show that if the coercivity rate of <span>(sigma )</span> lies in the range <span>(]frac{s+1}{s},(frac{s+1}{s})(2-frac{1}{n})])</span> with <span>(sin left( frac{n}{p}, infty right) cap left( frac{1}{p-1}, infty right) ,)</span> then <i>u</i> is approximately differentiable and the equation holds with <i>Du</i> replaced by <span>(text{ apDu })</span>. The proof relies on an approximation of <span>(mu )</span> by smooth functions <span>(f_{k})</span> and a compactness result for the corresponding solutions <span>(u_{k}.)</span> This follows from a detailed analysis of the Young measure <span>({delta _{u}(x)otimes vartheta (x)})</span> generated by the sequence <span>({(u_{k},Du_{k})})</span>, and the div-curl type inequality <span>(langle vartheta (x),sigma (x,u,cdot )rangle le overline{sigma }(x)langle vartheta (x),cdot rangle )</span> for the weak limit <span>(overline{sigma })</span> of the sequence.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"34 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-023-01117-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797550","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}