CuboPub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.139
Sepide Hajighasemi, S. Hejazian
{"title":"Surjective maps preserving the reduced minimum modulus of products","authors":"Sepide Hajighasemi, S. Hejazian","doi":"10.56754/0719-0646.2501.139","DOIUrl":"https://doi.org/10.56754/0719-0646.2501.139","url":null,"abstract":"Suppose $mathfrak{B}(H)$ is the Banach algebra of all bounded linear operators on a Hilbert space $H$ with $dim(H)geq 3$. Let $gamma(.)$ denote the reduced minimum modulus of an operator. We charaterize surjective maps $varphi$ on $mathfrak{B}(H)$ satisfying $$gamma(varphi(T)varphi(S))=gamma(T S);;;(T, Sin mathfrak{B}(H)).$$ Also, we give the general form of surjective maps on $mathfrak B(H)$ preserving the reduced minimum modulus of Jordan triple products of operators.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46679311","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}
CuboPub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.067
Ajay Kumar, Ekta Tamrakar
{"title":"Inertial algorithm for solving split inclusion problem in Banach spaces","authors":"Ajay Kumar, Ekta Tamrakar","doi":"10.56754/0719-0646.2501.067","DOIUrl":"https://doi.org/10.56754/0719-0646.2501.067","url":null,"abstract":"The purpose of this paper is to propose an algorithm for finding a common element of the set of fixed points of relatively nonexpansive mapping and the set of solutions of split inclusion problem with a way of selecting the stepsize without prior knowledge of the operator norm in the framework of Banach spaces. Then, the main result is used to the common fixed point problems of a family of relatively nonexpansive mappings and split equilibrium problem. Finally, a numerical example is provided to illustrate the main result.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41912624","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}
CuboPub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.023
B. Dhage, J. Graef, S. Dhage
{"title":"Existence, stability and global attractivity results for nonlinear Riemann-Liouville fractional differential equations","authors":"B. Dhage, J. Graef, S. Dhage","doi":"10.56754/0719-0646.2501.023","DOIUrl":"https://doi.org/10.56754/0719-0646.2501.023","url":null,"abstract":"Existence, attractivity, and stability of solutions of a non-linear fractional differential equation of Riemann-Liouville type are proved using the classical Schauder fixed point theorem and a fixed point result due to Dhage. The results are illustrated with examples.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48558168","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}
CuboPub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.089
O. Furdui, A. Sîntămărian
{"title":"Cubic and quartic series with the tail of $ln 2$","authors":"O. Furdui, A. Sîntămărian","doi":"10.56754/0719-0646.2501.089","DOIUrl":"https://doi.org/10.56754/0719-0646.2501.089","url":null,"abstract":"In this paper we calculate some remarkable cubic and quartic series involving the tail of ln2. We also evaluate several linear and quadratic series with the tail of ln2.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44613855","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}
CuboPub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.121
Liancheng Wang, Bo Yang
{"title":"New upper estimate for positive solutions to a second order boundary value problem with a parameter","authors":"Liancheng Wang, Bo Yang","doi":"10.56754/0719-0646.2501.121","DOIUrl":"https://doi.org/10.56754/0719-0646.2501.121","url":null,"abstract":"We consider a second order boundary value problem with a parameter. A new upper bound for positive solutions and Green’s function of the problem is obtained.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46532018","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}
CuboPub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.001
Said Ait Temghart, C. Allalou, Adil Abbassi
{"title":"Existence results for a class of local and nonlocal nonlinear elliptic problems","authors":"Said Ait Temghart, C. Allalou, Adil Abbassi","doi":"10.56754/0719-0646.2501.001","DOIUrl":"https://doi.org/10.56754/0719-0646.2501.001","url":null,"abstract":"In this paper, we study the $p$-Laplacian problems in the case where $p$ depends on the solution itself. We consider two situations, when $p$ is a local and nonlocal quantity. By using a singular perturbation technique, we prove the existence of weak solutions for the problem associated to the following equation $$ begin{cases} -mathrm{d}mathrm{i}mathrm{v}(|nabla u|^{p(u)-2}nabla u)+|u|^{p(u)-2}u=f & mbox{in}; Omega u=0& mbox{on}; partialOmega , end{cases}$$ and also for its nonlocal version. The main goal of this paper is to extend the results established by M. Chipot and H. B. de Oliveira (Math. Ann., 2019, 375, 283-306).","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46623044","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}
CuboPub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.037
Y. Raffoul
{"title":"Boundedness and stability in nonlinear systems of differential equations using a modified variation of parameters formula","authors":"Y. Raffoul","doi":"10.56754/0719-0646.2501.037","DOIUrl":"https://doi.org/10.56754/0719-0646.2501.037","url":null,"abstract":"In this research we introduce a new variation of parameters for systems of linear and nonlinear ordinary differential equations. We use known mathematical methods and techniques including Gronwall’s inequality and fixed point theory to obtain boundedness on all solutions and stability results on the zero solution.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48615155","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}
CuboPub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.151
Raúl Fierro, Sergio Pizarro
{"title":"Fixed points of set-valued mappings satisfying a Banach orbital condition","authors":"Raúl Fierro, Sergio Pizarro","doi":"10.56754/0719-0646.2501.151","DOIUrl":"https://doi.org/10.56754/0719-0646.2501.151","url":null,"abstract":"In this note, we prove a fixed point existence theorem for set-valued functions by extending the usual Banach orbital condition concept for single valued mappings. As we show, this result applies to various types of set-valued contractions existing in the literature.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43570790","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}
CuboPub Date : 2023-03-11DOI: 10.56754/0719-0646.2502.161
M. Bhardwaj, A. Osipov
{"title":"Some observations on a clopen version of the Rothberger property","authors":"M. Bhardwaj, A. Osipov","doi":"10.56754/0719-0646.2502.161","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.161","url":null,"abstract":"In this paper, we prove that a clopen version $S_1(mathcal{C}_mathcal{O}, mathcal{C}_mathcal{O})$ of the Rothberger property and Borel strong measure zeroness are independent. For a zero-dimensional metric space $(X,d)$, $X$ satisfies $S_1(mathcal{C}_mathcal{O}, mathcal{C}_mathcal{O})$ if, and only if, $X$ has Borel strong measure zero with respect to each metric which has the same topology as $d$ has. In a zero-dimensional space, the game $G_1(mathcal{O}, mathcal{O})$ is equivalent to the game $G_1(mathcal{C}_mathcal{O}, mathcal{C}_mathcal{O})$ and the point-open game is equivalent to the point-clopen game. Using reflections, we obtain that the game $G_1(mathcal{C}_mathcal{O}, mathcal{C}_mathcal{O})$ and the point-clopen game are strategically and Markov dual. An example is given for a space on which the game $G_1(mathcal{C}_mathcal{O}, mathcal{C}_mathcal{O})$ is undetermined.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42686314","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}
CuboPub Date : 2022-12-21DOI: 10.56754/0719-0646.2403.0457
Manuel Saavedra, H. Villavicencio
{"title":"On the minimum ergodic average and minimal systems","authors":"Manuel Saavedra, H. Villavicencio","doi":"10.56754/0719-0646.2403.0457","DOIUrl":"https://doi.org/10.56754/0719-0646.2403.0457","url":null,"abstract":"We prove some equivalences associated with the case when the average lower time is minimal. In addition, we characterize the minimal systems by means of the positivity of invariant measures on open sets and also the minimum ergodic averages. Finally, we show that a minimal system admits an open set whose measure is minimal with respect to a set of ergodic measures and its value can be chosen in [0, 1].","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48239461","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}