Pub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.139
Sepide Hajighasemi, S. Hejazian
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.
{"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}
Pub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.067
Ajay Kumar, Ekta Tamrakar
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.
{"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}
Pub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.023
B. Dhage, J. Graef, S. Dhage
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.
{"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}
Pub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.089
O. Furdui, A. Sîntămărian
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.
本文计算了一些涉及ln2尾部的显著的三次和四次级数。我们还计算了几个以ln2为尾的线性和二次级数。
{"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}
Pub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.121
Liancheng Wang, Bo Yang
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.
考虑一类带参数的二阶边值问题。得到了该问题正解和格林函数的一个新的上界。
{"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}
Pub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.001
Said Ait Temghart, C. Allalou, Adil Abbassi
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).
本文研究了$p$依赖于解本身的情况下的$p$ -拉普拉斯问题。我们考虑两种情况，其中$p$是一个局部量和一个非局部量。利用奇异摄动技术，我们证明了下述方程$$ begin{cases} -mathrm{d}mathrm{i}mathrm{v}(|nabla u|^{p(u)-2}nabla u)+|u|^{p(u)-2}u=f & mbox{in}; Omega u=0& mbox{on}; partialOmega , end{cases}$$及其非局部版本的弱解的存在性。本文的主要目的是推广M. Chipot和H. B. de Oliveira(数学)建立的结果。安。生物医学工程学报，2019,37(3):283-306。
{"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}
Pub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.037
Y. Raffoul
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.
{"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}
Pub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.151
Raúl Fierro, Sergio Pizarro
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.
{"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}
Pub Date : 2023-03-11DOI: 10.56754/0719-0646.2502.161
M. Bhardwaj, A. Osipov
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.
{"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}
Pub Date : 2022-12-21DOI: 10.56754/0719-0646.2403.0457
Manuel Saavedra, H. Villavicencio
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].
{"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}
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