In this paper, we introduce a new class of subsets of class bounded linear operators between Banach spaces which is called p-(DPL) sets. Then, the relationship between these sets with equicompact sets is investigated. Moreover, we define p-version of Right sequentially continuous differentiable mappings and get some characterizations of these mappings. Finally, we prove that a mapping f : X ? Y between real Banach spaces is Fr?chet differentiable and f? takes bounded sets into p-(DPL) sets if and only if f may be written in the form f = 1?S where the intermediate space is normed, S is a Dunford-Pettis p-convergent operator, and g is a G?teaux differentiable mapping with some additional properties.
本文引入了Banach空间间一类有界线性算子的一个新的子集，称为p-(DPL)集。然后，研究了这些集合与等紧集合之间的关系。此外，我们定义了右序列连续可微映射的p型，并得到了这些映射的一些刻画。最后，我们证明了映射f: X ?实巴拿赫空间之间的Y等于Fr?可微的和f?取有界集合为p-(DPL)集合当且仅当f可以写成f = 1?S，其中中间空间是赋范的，S是Dunford-Pettis p收敛算子，g是g ?具有一些附加性质的托可微映射。
{"title":"Some applications of p-(DPL) sets","authors":"M. Alikhani","doi":"10.2298/fil2305367a","DOIUrl":"https://doi.org/10.2298/fil2305367a","url":null,"abstract":"In this paper, we introduce a new class of subsets of class bounded linear operators between Banach spaces which is called p-(DPL) sets. Then, the relationship between these sets with equicompact sets is investigated. Moreover, we define p-version of Right sequentially continuous differentiable mappings and get some characterizations of these mappings. Finally, we prove that a mapping f : X ? Y between real Banach spaces is Fr?chet differentiable and f? takes bounded sets into p-(DPL) sets if and only if f may be written in the form f = 1?S where the intermediate space is normed, S is a Dunford-Pettis p-convergent operator, and g is a G?teaux differentiable mapping with some additional properties.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68269651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This manuscript discusses the existence of nontrivial weak solution for the following nonlinear eigenvalue problem driven by the p(?)-biharmonic operator with Rellich-type term {?(|?u|p(x)?2?u) = ?|u|q(x)?2u/?(x)2q(x), for x ? ?, u = ?u = 0, for x ? ??. Considering the case 1 < min x?? p(x) ? max x?? p(x) < min x?? q(x) ? max x?? q(x) < min (N 2, Np(x) N ? 2p(x) ), we extend the corresponding result of the reference [8], for the case 1 < min x?? q(x) ? max x?? q(x) < min x?? p(x) ? max x?? .p(x) < N 2 . The proofs of the main results are based on the mountain pass theorem
本文讨论了具有rellich型项{?(|?u|p(x)?2?u) = ?|u|q(x)?2u/?(x)2q(x)的p(?)-双调和算子驱动下的非线性特征值问题非平凡弱解的存在性，对于x ?， u = ?u = 0，对于x ?? ?。考虑1 < min x??p (x) ?最大x ? ?P (x) < min x??问(x) ?最大x ? ?q(x) < min (n2, Np(x) N ?2p(x))，我们扩展了参考[8]的相应结果，对于1 < min x?? ?问(x) ?最大x ? ?Q (x) < min x??p (x) ?最大x ? ?.p(x) < N主要结果的证明是基于山口定理的
{"title":"Existence of mountain-pass solutions for p(・)-biharmonic equations with Rellich-type term","authors":"Mohamed Laghzal, A. Touzani","doi":"10.2298/fil2305549l","DOIUrl":"https://doi.org/10.2298/fil2305549l","url":null,"abstract":"This manuscript discusses the existence of nontrivial weak solution for the following nonlinear eigenvalue problem driven by the p(?)-biharmonic operator with Rellich-type term {?(|?u|p(x)?2?u) = ?|u|q(x)?2u/?(x)2q(x), for x ? ?, u = ?u = 0, for x ? ??. Considering the case 1 < min x?? p(x) ? max x?? p(x) < min x?? q(x) ? max x?? q(x) < min (N 2, Np(x) N ? 2p(x) ), we extend the corresponding result of the reference [8], for the case 1 < min x?? q(x) ? max x?? q(x) < min x?? p(x) ? max x?? .p(x) < N 2 . The proofs of the main results are based on the mountain pass theorem","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68269748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a class of complex-valued neural networks with time-varying delays is studied. By employing an extension of Mawhin?s continuation theorem and an approximation technique, several sufficient conditions of the new results on the existence of homoclinic solutions and periodic solutions are established. Moreover, the asymptotic behavior of solutions via the Lyapunov function is also investigated. Finally, for the purpose of validity, an example is given to illustrate the effectiveness of main results.
{"title":"Homoclinic solutions and periodic solutions of complex-valued neural networks with time-varying delays","authors":"Ling Sun, F. Kong","doi":"10.2298/fil2307997s","DOIUrl":"https://doi.org/10.2298/fil2307997s","url":null,"abstract":"In this paper, a class of complex-valued neural networks with time-varying delays is studied. By employing an extension of Mawhin?s continuation theorem and an approximation technique, several sufficient conditions of the new results on the existence of homoclinic solutions and periodic solutions are established. Moreover, the asymptotic behavior of solutions via the Lyapunov function is also investigated. Finally, for the purpose of validity, an example is given to illustrate the effectiveness of main results.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68272586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we prove that an almost Kenmotsu manifold M has constant Reeb sectional curvatures if and only if M has conformal Reeb foliation. Onan almost Kenmotsu h-a-manifold of dimension three having constant ?-sectional curvature, the Reeb vector field is an eigenvector field of the Ricci operator if and only if the manifold is locally isometric to a non-unimodular Lie group.
{"title":"Almost Kenmotsu manifolds with constant Reeb or Ф-sectional curvatures","authors":"Yaning Wang, Pei Wang","doi":"10.2298/fil2308495w","DOIUrl":"https://doi.org/10.2298/fil2308495w","url":null,"abstract":"In this paper, we prove that an almost Kenmotsu manifold M has constant Reeb sectional curvatures if and only if M has conformal Reeb foliation. Onan almost Kenmotsu h-a-manifold of dimension three having constant ?-sectional curvature, the Reeb vector field is an eigenvector field of the Ricci operator if and only if the manifold is locally isometric to a non-unimodular Lie group.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68275522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LetH be a real or complex Hilbert space with dim(H) > 1, B(H) be algebra of all bounded linear operators on H and A(H) ? B(H) be a standard operator algebra on H. If D : A(H) ? B(H) is a linear mapping satisfying D(An+1) = Pn i=0 AiD(A)(A*)n?i for all A ? A(H), then D is a Jordan *-derivation on A(H). Later, we discuss some algebraic identities on semiprime rings.
LetH是一个实数或复希尔伯特空间，其中dim(H) >1, B(H)是H和a (H)上所有有界线性算子的代数?B(H)是H上的标准算子代数，如果D: a (H) ?B(H)是一个线性映射，满足D(An+1) = Pn i=0 AiD(a)(a *)n?i for all A ?A(H)那么D是A(H)的约当导数。随后，我们讨论了半素环上的一些代数恒等式。
{"title":"Jordan *-derivations on standard operator algebras","authors":"A. Ansari, F. Shujat","doi":"10.2298/fil2301037a","DOIUrl":"https://doi.org/10.2298/fil2301037a","url":null,"abstract":"LetH be a real or complex Hilbert space with dim(H) > 1, B(H) be algebra of all bounded linear operators on H and A(H) ? B(H) be a standard operator algebra on H. If D : A(H) ? B(H) is a linear mapping satisfying D(An+1) = Pn i=0 AiD(A)(A*)n?i for all A ? A(H), then D is a Jordan *-derivation on A(H). Later, we discuss some algebraic identities on semiprime rings.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68266084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As the real common generalisations of both orthodox transversals and adequate transversals in abundant semigroups, the concept of refined generalised quasi-adequate transversals, briefly, RGQA transversals was introduced by Kong and Wang. In this paper, for the RGQA transversal, the necessary and sufficient condition for the sets I and ? to be bands is investigated. It is demonstrated that the sets I and ? are both bands if and only if the RGQA transversal is weakly simplistic. Moreover, the RGQA transversal So being weakly simplistic is different from So being a quasi-ideal nor the abundant semigroup S satisfying the regularity condition. Finally, by means of a quasi-adequate semigroup and a band, the structure theorem for an abundant semigroup with a weakly simplistic RGQA transversal is established.
{"title":"Abundant semigroups with weakly simplistic RGQA transversals","authors":"Pei Wang, Xiangjun Kong","doi":"10.2298/fil2301155w","DOIUrl":"https://doi.org/10.2298/fil2301155w","url":null,"abstract":"As the real common generalisations of both orthodox transversals and adequate transversals in abundant semigroups, the concept of refined generalised quasi-adequate transversals, briefly, RGQA transversals was introduced by Kong and Wang. In this paper, for the RGQA transversal, the necessary and sufficient condition for the sets I and ? to be bands is investigated. It is demonstrated that the sets I and ? are both bands if and only if the RGQA transversal is weakly simplistic. Moreover, the RGQA transversal So being weakly simplistic is different from So being a quasi-ideal nor the abundant semigroup S satisfying the regularity condition. Finally, by means of a quasi-adequate semigroup and a band, the structure theorem for an abundant semigroup with a weakly simplistic RGQA transversal is established.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68266534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the case of linear operator the property P(B, k) was introduced by M.A. Kaashoek. In this paper, we characterize the essentially semi regular linear relation in terms of the property P(B, k). After that and as an application of this result we give some connection between essentially semi regular and semi regular linear relations. Further, we will give some supplementary conditions on essentially semi regular linear relation to be semi Fredholm. Then, we analyze the stability of the class of essentially semi regular linear relations under small perturbations and Riesz operators. Finally, we study some properties of the essentially semi regular spectrum of a linear relation and we establish a spectral mapping theorem.
{"title":"Representation of essentially semi regular linear relations and perturbations","authors":"Sonia Keskes, M. Mnif","doi":"10.2298/fil2302443k","DOIUrl":"https://doi.org/10.2298/fil2302443k","url":null,"abstract":"In the case of linear operator the property P(B, k) was introduced by M.A. Kaashoek. In this paper, we characterize the essentially semi regular linear relation in terms of the property P(B, k). After that and as an application of this result we give some connection between essentially semi regular and semi regular linear relations. Further, we will give some supplementary conditions on essentially semi regular linear relation to be semi Fredholm. Then, we analyze the stability of the class of essentially semi regular linear relations under small perturbations and Riesz operators. Finally, we study some properties of the essentially semi regular spectrum of a linear relation and we establish a spectral mapping theorem.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68266972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we establish exponential inequalities which allow us to construct confidence regions, characterized by ellipses, for the least squares estimates of the parameters in the case of a linear regression model with ?-mixing errors.
{"title":"Confidence ellipses for simple regression parameters with strongly mixing errors","authors":"Abdelkader Elmoumen, Halima Zerouati, A. Dahmani","doi":"10.2298/fil2302591e","DOIUrl":"https://doi.org/10.2298/fil2302591e","url":null,"abstract":"In this work, we establish exponential inequalities which allow us to construct confidence regions, characterized by ellipses, for the least squares estimates of the parameters in the case of a linear regression model with ?-mixing errors.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68267274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is devoted to the investigation of the generalized implicit equilibrium problems with weak conditions in general space. Sufficient conditions for the set of solutions to be compact and convex are given. Our results improve some recent results in this field.
{"title":"On generalized implicit equilibrium problems","authors":"A. Farajzadeh, P. Zangenehmehr","doi":"10.2298/fil2303689f","DOIUrl":"https://doi.org/10.2298/fil2303689f","url":null,"abstract":"This paper is devoted to the investigation of the generalized implicit equilibrium problems with weak conditions in general space. Sufficient conditions for the set of solutions to be compact and convex are given. Our results improve some recent results in this field.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68267620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In complex two-plane Grassmannians G2(Cm+2) = SU2+m/S(U2?Um), it is known that a real hypersurface satisfying the condition (L?(k)?R?)Y = (L?R?)Y is locally congruent to an open part of a tube around a totally geodesic G2(Cm+1) in G2(Cm+2). In this paper, as an abient space, we consider a complex hyperbolic two-plane Grassmannian SU2,m/S(U2?Um) and give a complete classification of Hopf real hypersurfaces in SU2,m/S(U2?Um) with the above condition.
在复两平面格拉斯曼曲面G2(Cm+2) = SU2+m/S(U2?Um)中，已知实超曲面满足条件(L?(k)?R?)Y = (l ? r ?)在G2(Cm+2)中，Y局部与完全测地线G2(Cm+1)周围的管的开口部分相等。本文将复双曲型两平面Grassmannian SU2,m/S(U2?Um)作为一个不存在空间，利用上述条件给出了SU2,m/S(U2?Um)上的Hopf实超曲面的完全分类。
{"title":"Reeb lie derivatives on real hypersurfaces in complex hyperbolic two-plane Grassmannians","authors":"Eunmi Pak, G. Kim","doi":"10.2298/fil2303915p","DOIUrl":"https://doi.org/10.2298/fil2303915p","url":null,"abstract":"In complex two-plane Grassmannians G2(Cm+2) = SU2+m/S(U2?Um), it is known that a real hypersurface satisfying the condition (L?(k)?R?)Y = (L?R?)Y is locally congruent to an open part of a tube around a totally geodesic G2(Cm+1) in G2(Cm+2). In this paper, as an abient space, we consider a complex hyperbolic two-plane Grassmannian SU2,m/S(U2?Um) and give a complete classification of Hopf real hypersurfaces in SU2,m/S(U2?Um) with the above condition.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68268086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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