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On generalized Hardy spaces associated with singular partial differential operators 与奇异偏微分算子相关的广义Hardy空间
IF 0.5
Cubo Pub Date : 2023-08-28 DOI: 10.56754/0719-0646.2502.289
A. Ghandouri, H. Mejjaoli, S. Omri
{"title":"On generalized Hardy spaces associated with singular partial differential operators","authors":"A. Ghandouri, H. Mejjaoli, S. Omri","doi":"10.56754/0719-0646.2502.289","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.289","url":null,"abstract":"We define and study the Hardy spaces associated with singular partial differential operators. Also, a characterization by mean of atomic decomposition is investigated.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46750227","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: 1
Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem 利用不动点定理研究三叉Banach代数三叉不定导数的稳定性
IF 0.5
Cubo Pub Date : 2023-08-09 DOI: 10.56754/0719-0646.2502.273
Mehdi Dehghanian, Choonkill Park, Y. Sayyari
{"title":"Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem","authors":"Mehdi Dehghanian, Choonkill Park, Y. Sayyari","doi":"10.56754/0719-0646.2502.273","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.273","url":null,"abstract":"In this paper, we introduce the concept of ternary antiderivation on ternary Banach algebras and investigate the stability of ternary antiderivation in ternary Banach algebras, associated to the $(alpha,beta)$-functional inequality: begin{align*} &Vert mathcal{F}(x+y+z)-mathcal{F}(x+z)-mathcal{F}(y-x+z)-mathcal{F}(x-z)Vert nonumber &leq Vert alpha (mathcal{F}(x+y-z)+mathcal{F}(x-z)-mathcal{F}(y))Vert + Vert beta (mathcal{F}(x-z) &+mathcal{F}(x)-mathcal{F}(z))Vert end{align*} where $alpha$ and $beta$ are fixed nonzero complex numbers with $vertalpha vert +vert beta vert<2$ by using the fixed point method.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43820847","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
Maximum, anti-maximum principles and monotone methods for boundary value problems for Riemann-Liouville fractional differential equations in neighborhoods of simple eigenvalues 黎曼-刘维尔分数阶微分方程边值问题的极大值、反极大值原理和单调方法
IF 0.5
Cubo Pub Date : 2023-08-07 DOI: 10.56754/0719-0646.2502.251
P. Eloe, Jeffrey T. Neugebauer
{"title":"Maximum, anti-maximum principles and monotone methods for boundary value problems for Riemann-Liouville fractional differential equations in neighborhoods of simple eigenvalues","authors":"P. Eloe, Jeffrey T. Neugebauer","doi":"10.56754/0719-0646.2502.251","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.251","url":null,"abstract":"It has been shown that, under suitable hypotheses, boundary value problems of the form, $Ly+lambda y=f,$ $BC y =0$ where $L$ is a linear ordinary or partial differential operator and $BC$ denotes a linear boundary operator, then there exists $Lambda >0$ such that $fge 0$ implies $lambda y ge 0$ for $lambdain [-Lambda ,Lambda ]setminus{0},$ where $y$ is the unique solution of $Ly+lambda y=f,$ $BC y =0$. So, the boundary value problem satisfies a maximum principle for $lambdain [-Lambda ,0)$ and the boundary value problem satisfies an anti-maximum principle for $lambdain (0, Lambda ]$. In an abstract result, we shall provide suitable hypotheses such that boundary value problems of the form, $D_{0}^{alpha}y+beta D_{0}^{alpha -1}y=f,$ $BC y =0$ where $D_{0}^{alpha}$ is a Riemann-Liouville fractional differentiable operator of order $alpha$, $1<alpha le 2$, and $BC$ denotes a linear boundary operator, then there exists $mathcal{B} >0$ such that $fge 0$ implies $beta D_{0}^{alpha -1}y ge 0$ for $beta in [-mathcal{B} ,mathcal{B} ]setminus{0},$ where $y$ is the unique solution of $D_{0}^{alpha}y+beta D_{0}^{alpha -1}y =f,$ $BC y =0$. Two examples are provided in which the hypotheses of the abstract theorem are satisfied to obtain the sign property of $beta D_{0}^{alpha -1}y.$ The boundary conditions are chosen so that with further analysis a sign property of $beta y$ is also obtained. One application of monotone methods is developed to illustrate the utility of the abstract result.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43858847","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
Existence and controllability of integrodifferential equations with non-instantaneous impulses in Fréchet spaces fr<s:1>空间中非瞬时脉冲积分微分方程的存在性和可控性
IF 0.5
Cubo Pub Date : 2023-08-05 DOI: 10.56754/0719-0646.2502.231
A. Bensalem, Abdelkrim Salim, B. Ahmad, M. Benchohra
{"title":"Existence and controllability of integrodifferential equations with non-instantaneous impulses in Fréchet spaces","authors":"A. Bensalem, Abdelkrim Salim, B. Ahmad, M. Benchohra","doi":"10.56754/0719-0646.2502.231","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.231","url":null,"abstract":"In this paper, we investigate existence of mild solutions to a non-instantaneous integrodifferential equation via resolvent operators in the sense of Grimmer in Fréchet spaces. Utilizing the technique of measures of noncompactness in conjunction with the Darbo's fixed point theorem, we present sufficient criteria ensuring the controllability of the given problem. An illustrative example is also discussed.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44889535","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 stability of nonlocal neutral stochastic integro differential equations with random impulses and Poisson jumps 具有随机脉冲和泊松跳的非局部中立型随机积分微分方程的稳定性
IF 0.5
Cubo Pub Date : 2023-08-04 DOI: 10.56754/0719-0646.2502.211
Sahar M. A. Maqbol, R. S. Jain, B. Reddy
{"title":"On stability of nonlocal neutral stochastic integro differential equations with random impulses and Poisson jumps","authors":"Sahar M. A. Maqbol, R. S. Jain, B. Reddy","doi":"10.56754/0719-0646.2502.211","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.211","url":null,"abstract":"This article aims to examine the existence and Hyers-Ulam stability of non-local random impulsive neutral stochastic integrodifferential delayed equations with Poisson jumps. Initially, we prove the existence of mild solutions to the equations by using the Banach fixed point theorem. Then, we investigate stability via the continuous dependence of solutions on the initial value. Next, we study the Hyers-Ulam stability results under the Lipschitz condition on a bounded and closed interval. Finally, we give an illustrative example of our main result.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49215480","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
Osculating varieties and their joins: $mathbb{P}^1times mathbb{P}^1$ 密切品种及其联接：$mathbb｛P｝^1 timesmathbb｛P}^1$
IF 0.5
Cubo Pub Date : 2023-08-01 DOI: 10.56754/0719-0646.2502.331
E. Ballico
{"title":"Osculating varieties and their joins: $mathbb{P}^1times mathbb{P}^1$","authors":"E. Ballico","doi":"10.56754/0719-0646.2502.331","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.331","url":null,"abstract":"Let $Xsubset PP^r$ be an integral projective variety. We study the dimensions of the joins of several copies of the osculating varieties $J(X,m)$ of $X$. Our methods are general, but we give a full description in all cases only if $X$ is a linearly normal embedding of $PP^1times PP^1$. For these embeddings of $PP^1times PP^1$ we give several examples and then study the joins of one copy of $J(X,m)$ and an arbitrary number of copies of $X$.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41427504","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
Laeng-Morpurgo-type uncertainty inequalities for the Weinstein transform Weinstein变换的Laeng-Morpugo型不确定性不等式
IF 0.5
Cubo Pub Date : 2023-08-01 DOI: 10.56754/0719-0646.2502.321
F. Soltani, Slim Ben Rejeb
{"title":"Laeng-Morpurgo-type uncertainty inequalities for the Weinstein transform","authors":"F. Soltani, Slim Ben Rejeb","doi":"10.56754/0719-0646.2502.321","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.321","url":null,"abstract":"In this work, by combining Carlson-type and Nash-type inequalities for the Weinstein transform $mathscr{F}_W$ on $mathbb{K}=mathbb{R}^{d-1}times[0,infty)$, we show Laeng-Morpurgo-type uncertainty inequalities. We establish also local-type uncertainty inequalities for the Weinstein transform $mathscr{F}_W$, and we deduce a Heisenberg-Pauli-Weyl-type inequality for this transform.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45178958","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
Several inequalities for an integral transform of positive operators in Hilbert spaces with applications Hilbert空间中正算子积分变换的几个不等式及其应用
IF 0.5
Cubo Pub Date : 2023-07-19 DOI: 10.56754/0719-0646.2502.195
S. Dragomir, S. S. Dragomir
{"title":"Several inequalities for an integral transform of positive operators in Hilbert spaces with applications","authors":"S. Dragomir, S. S. Dragomir","doi":"10.56754/0719-0646.2502.195","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.195","url":null,"abstract":"For a continuous and positive function (wleft( lambda right) ,) (lambda>0) and (mu ) a positive measure on ((0,infty )) we consider the following Integral Transform [ begin{equation*} mathcal{D}left( w,mu right) left( Tright) :=int_{0}^{infty }wleft(lambda right) left( lambda +Tright)^{-1}dmu left( lambda right) , end{equation*} ] where the integral is assumed to exist for (T) a postive operator on a complex Hilbert space (H). We show among others that, if ( beta geq A geq alpha > 0, , B > 0 ) with ( M geq B-A geq m > 0 ) for some constants ( alpha,  beta,  m,  M ), then [ begin{align*} 0 & leq frac{m^{2}}{M^{2}}left[ mathcal{D}left( w,mu right) left(betaright) - mathcal{D}left( w,mu right) left(M+betaright) right] & leq frac{m^{2}}{M}left[ mathcal{D}left( w,mu right) left(betaright) - mathcal{D}left( w,mu right) left(M+betaright) right] left( B-Aright)^{-1} & leq mathcal{D}left( w,mu right) left(Aright) - mathcal{D}left(w,muright) left(Bright) & leq frac{M^{2}}{m}left[ mathcal{D}left( w,mu right) left(alpharight) - mathcal{D}left( w,mu right) left(m+alpharight) right] left(B-Aright)^{-1} & leq frac{M^{2}}{m^{2}}left[ mathcal{D}left( w,mu right) left(alpharight) - mathcal{D}left( w,mu right) left(m+alpharight) right]. end{align*} ] Some examples for operator monotone and operator convex functions as well as for integral transforms (mathcal{D}left( cdot ,cdot right) ) related to the exponential and logarithmic functions are also provided.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48523841","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
Existence of solutions for higher order $phi-$Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions 利用具有无序上下解的单侧Nagumo条件证明半线上高阶$ φ -$拉普拉斯算子解的存在性
IF 0.5
Cubo Pub Date : 2023-07-19 DOI: 10.56754/0719-0646.2502.173
A. Zerki, K. Bachouche, K. Ait-Mahiout
{"title":"Existence of solutions for higher order $phi-$Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions","authors":"A. Zerki, K. Bachouche, K. Ait-Mahiout","doi":"10.56754/0719-0646.2502.173","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.173","url":null,"abstract":"In this paper, we consider the following ((n+1))st order bvp on the half line with a (phi-)Laplacian operator [ begin{cases} (phi(u^{(n)}))'(t) = f(t,u(t),ldots,u^{(n)}(t)), & text{a.e.},, tin [0,+infty), n in mathbb{N}setminus{0},   u^{(i)}(0) = A_{i}, , i=0,ldots,n-2, u^{(n-1)}(0) + au^{(n)}(0) = B, u^{(n)}(+infty) = C. end{cases} ] The existence of solutions is obtained by applying Schaefer's fixed point theorem under a one-sided Nagumo condition with nonordered lower and upper solutions method where (f) is a (L^{1})-Carathéodory function.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44413330","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
Some critical remarks on recent results concerning $digamma-$contractions in $b$-metric spaces 关于$b$-度量空间中$digamma-$收缩的最近结果的一些批评性意见
IF 0.5
Cubo Pub Date : 2023-04-20 DOI: 10.56754/0719-0646.2501.057
Mudasir Younis, Nikola Mirkov, A. Savić, M. Pantović, S. Radenović
{"title":"Some critical remarks on recent results concerning $digamma-$contractions in $b$-metric spaces","authors":"Mudasir Younis, Nikola Mirkov, A. Savić, M. Pantović, S. Radenović","doi":"10.56754/0719-0646.2501.057","DOIUrl":"https://doi.org/10.56754/0719-0646.2501.057","url":null,"abstract":"This paper aims to correct recent results on a generalized class of $digamma-$contractions in the context of $b-$metric spaces. The significant work consists of repairing some novel results involving $digamma-$contraction within the structure of $b$-metric spaces. Our objective is to take advantage of the property $(F1)$ instead of the four properties viz. $(F1)$, $(F2)$, $(F3)$ and $(F4)$ applied in the results of Nazam textit{et al.} [``Coincidence and common fixed point theorems for four mappings satisfying $(alpha_s,F)-$contraction\", Nonlinear Anal: Model. Control., vol. 23, no. 5, pp. 664--690, 2018]. Our approach of proving the results utilizing only the condition $(F1)$ enriches, improves, and condenses the proofs of a multitude of results in the existing state-of-art.","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":"43315555","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
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