In this paperwe investigate the spectrum and the Drazin spectrum and their pseudo spectral analogues, for linear relations between Banach spaces and corresponding spectra, the generalized Drazinmeromorphic pseudospectrum. More specifically, the generalized Drazin-meromorphic pseudospectrum for a linear relations on a Banach space is studied. We also make several observations about the level set of the generalized Drazin-meromorphic pseudospectrum of linear relations. Furthermore, it is shown that pseudospectrum has no isolated points, has a finite number of connected components and each component contains an element from the generalized Drazin-meromorphic spectrum.
{"title":"Generalized Drazin-meromorphic pseudospectrum for multivalued linear relation","authors":"K. Mahfoudhi, B. Saadaoui, V. Rakočević","doi":"10.2298/fil2301193m","DOIUrl":"https://doi.org/10.2298/fil2301193m","url":null,"abstract":"In this paperwe investigate the spectrum and the Drazin spectrum and their pseudo spectral analogues, for linear relations between Banach spaces and corresponding spectra, the generalized Drazinmeromorphic pseudospectrum. More specifically, the generalized Drazin-meromorphic pseudospectrum for a linear relations on a Banach space is studied. We also make several observations about the level set of the generalized Drazin-meromorphic pseudospectrum of linear relations. Furthermore, it is shown that pseudospectrum has no isolated points, has a finite number of connected components and each component contains an element from the generalized Drazin-meromorphic spectrum.","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":"68266689","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 show a multiple-term refinement of Young?s type inequality and its reverse via the Kantorovich constants, which extends and unifies two recent and important results due to L. Nasiri et al. (Result. Math (74), 2019), and C. Yang et al. (Journal. Math. Inequalities, (14), 2020). An application of these scalars results we give a multiple-term refinement of Young?s type inequalities for operators, Hilbert-Schmidt norms, traces and the unitarily invariant norms.
{"title":"Further refinement of Young’s type inequalities and its reversed using the Kantorovich constants","authors":"M. Ighachane, M. Akkouchi","doi":"10.2298/fil2303675i","DOIUrl":"https://doi.org/10.2298/fil2303675i","url":null,"abstract":"In this paper, we show a multiple-term refinement of Young?s type inequality and its reverse via the Kantorovich constants, which extends and unifies two recent and important results due to L. Nasiri et al. (Result. Math (74), 2019), and C. Yang et al. (Journal. Math. Inequalities, (14), 2020). An application of these scalars results we give a multiple-term refinement of Young?s type inequalities for operators, Hilbert-Schmidt norms, traces and the unitarily invariant norms.","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":"68267566","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 derive Abelian theorems for the operators with complex Gaussian kernels. Specifically, we establish some results in which known the behaviour of the function and its domain variable approaches to ?? or +? is used to infer the asymptotic behaviour of the transform as its domain variable approaches to +? or ??. For this purpose we use a formula concerning the computation of potential functions by means of these operators with complex Gaussian kernels. This formula allows us to analyse the asymptotic behaviour of these operators in both cases: when the variable approaches to +? or ??. Our results include systematically the noncentered and centered cases of these operators. Here we analyse the Gauss-Weierstrass semigroup on R as a particular case. We also point out Abelian theorems for other kinds of operators which have been studied in several papers.
{"title":"Operators with complex Gaussian kernels: Asymptotic behaviours","authors":"B. J. González, E. Negrín","doi":"10.2298/fil2303833g","DOIUrl":"https://doi.org/10.2298/fil2303833g","url":null,"abstract":"In this paper we derive Abelian theorems for the operators with complex Gaussian kernels. Specifically, we establish some results in which known the behaviour of the function and its domain variable approaches to ?? or +? is used to infer the asymptotic behaviour of the transform as its domain variable approaches to +? or ??. For this purpose we use a formula concerning the computation of potential functions by means of these operators with complex Gaussian kernels. This formula allows us to analyse the asymptotic behaviour of these operators in both cases: when the variable approaches to +? or ??. Our results include systematically the noncentered and centered cases of these operators. Here we analyse the Gauss-Weierstrass semigroup on R as a particular case. We also point out Abelian theorems for other kinds of operators which have been studied in several papers.","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":"68267801","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 develops the notion of relative demicompact elements of an algebra with respect to a Banach subalgebra as a generalization of relative demicompact linear operators acting on Banach spaces. Drawing on this novel notion, we build a new class of Fredholm perturbation regarding a given Banach subalgebra B which contains its inessential ideal kB and the set of left Fredholm perturbations suggested in [6]. The developed class of Fredholm perturbation exhibits that is a two-sided closed ideal of B that is key in the characterization of the weyl spectrum of elements affiliated with B.
{"title":"Stability of relative essential spectra involving relative demicompactness concept in Banach subalgebra","authors":"Slim Chelly","doi":"10.2298/fil2303891c","DOIUrl":"https://doi.org/10.2298/fil2303891c","url":null,"abstract":"This paper develops the notion of relative demicompact elements of an algebra with respect to a Banach subalgebra as a generalization of relative demicompact linear operators acting on Banach spaces. Drawing on this novel notion, we build a new class of Fredholm perturbation regarding a given Banach subalgebra B which contains its inessential ideal kB and the set of left Fredholm perturbations suggested in [6]. The developed class of Fredholm perturbation exhibits that is a two-sided closed ideal of B that is key in the characterization of the weyl spectrum of elements affiliated with B.","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":"68267953","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 deals with the existence and global stability of solutions of a new class of Volterra partial integral equations of Hadamard-Stieltjes fractional order.
{"title":"Existence and global stability results for Volterra type fractional Hadamard-Stieltjes partial integral equations","authors":"S. Abbas, A. Arara, M. Benchohra","doi":"10.2298/fil2305319a","DOIUrl":"https://doi.org/10.2298/fil2305319a","url":null,"abstract":"This paper deals with the existence and global stability of solutions of a new class of Volterra partial integral equations of Hadamard-Stieltjes fractional order.","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":"68268755","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 the degree of approximation of the function f, which is periodic with respect to the hexagon lattice by matrix means T(A)n(f) of its hexagonal Fourier series in the generalized H?lder metric, where A is a lower triangular infinite matrix of nonnegative real numbers with nonincreasing row is estimated.
{"title":"Approximation by matrix means on hexagonal domains in the generalized Hölder metric","authors":"H. Aslan","doi":"10.2298/fil2304291a","DOIUrl":"https://doi.org/10.2298/fil2304291a","url":null,"abstract":"In this paper the degree of approximation of the function f, which is periodic with respect to the hexagon lattice by matrix means T(A)n(f) of its hexagonal Fourier series in the generalized H?lder metric, where A is a lower triangular infinite matrix of nonnegative real numbers with nonincreasing row is estimated.","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":"68268852","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 article we define a new class of topological spaces called para ?-discrete spaces and give an internal characterization of a subgroup of product of para ?-discrete semitopological groups having character less than or equal to ?. Also we give a partial solution of an open problem posed by S?nchez [5, Problem 3.8].
{"title":"Subgroups of products of para τ-discrete semitopological groups","authors":"Vikesh Kumar, B. Tyagi","doi":"10.2298/fil2307165k","DOIUrl":"https://doi.org/10.2298/fil2307165k","url":null,"abstract":"In this article we define a new class of topological spaces called para ?-discrete spaces and give an internal characterization of a subgroup of product of para ?-discrete semitopological groups having character less than or equal to ?. Also we give a partial solution of an open problem posed by S?nchez [5, Problem 3.8].","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":"68271938","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 introduce and study the S-pseudospectra of linear operators defined by nonstrict inequality in a Hilbert space. Inspired by A. B?ttcher?s result [3], we prove that the S-resolvent norm of bounded linear operators is not constant in any open set of the S-resolvent set. Beside, we find a characterization of the S-pseudospectrum of bounded linear operator by means the S-spectra of all perturbed operators with perturbations that have norms strictly less than ?.
{"title":"A characterization of S-pseudospectra of linear operators in a Hilbert space","authors":"A. Ammar, Ameni Bouchekoua, A. Jeribi","doi":"10.2298/fil2305331a","DOIUrl":"https://doi.org/10.2298/fil2305331a","url":null,"abstract":"In this work, we introduce and study the S-pseudospectra of linear operators defined by nonstrict inequality in a Hilbert space. Inspired by A. B?ttcher?s result [3], we prove that the S-resolvent norm of bounded linear operators is not constant in any open set of the S-resolvent set. Beside, we find a characterization of the S-pseudospectrum of bounded linear operator by means the S-spectra of all perturbed operators with perturbations that have norms strictly less than ?.","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":"68269449","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}
R. Ameziane Hassani, A. Blali, A. El amrani, Beldi El
The goal of this work is to introduce the two-parameter conformable fractional semigroups and provide a definition of its infinitesimal generator. For such generators, we develop multiple results. In addition, we show that the two-parameter conformable fractional semigroups provide a solution for two-parameter conformable fractional abstract Cauchy problems.
{"title":"Two-parameter conformable fractional semigroups and abstract Cauchy problems","authors":"R. Ameziane Hassani, A. Blali, A. El amrani, Beldi El","doi":"10.2298/fil2308303a","DOIUrl":"https://doi.org/10.2298/fil2308303a","url":null,"abstract":"The goal of this work is to introduce the two-parameter conformable fractional semigroups and provide a definition of its infinitesimal generator. For such generators, we develop multiple results. In addition, we show that the two-parameter conformable fractional semigroups provide a solution for two-parameter conformable fractional abstract Cauchy problems.","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":"68272890","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, due to the Borel lemma and Clunie lemma, we will deduce the relationship between an entire function f of hyper-order less than 1 and its n-th difference operator ?nc f (z) if they share a finite set and f has a Borel exceptional value 0, where the set consists of two entire functions of smaller orders. Moreover, the exact form of f is given and an example is provided to show the sharpness of the condition.
本文利用Borel引理和Clunie引理，推导出一个超阶小于1的完整函数f与它的第n个差分算子?nc f (z)之间的关系，如果它们共享一个有限集，并且f有一个Borel例外值0，其中该集合由两个较小阶的完整函数组成。此外，还给出了f的精确形式，并举例说明了条件的尖锐性。
{"title":"A study on entire functions of hyper-order sharing a finite set with their high-order difference operators","authors":"Hong-Fang Guo, F. Lü, W. Lü","doi":"10.2298/fil2302417g","DOIUrl":"https://doi.org/10.2298/fil2302417g","url":null,"abstract":"In this paper, due to the Borel lemma and Clunie lemma, we will deduce the relationship between an entire function f of hyper-order less than 1 and its n-th difference operator ?nc f (z) if they share a finite set and f has a Borel exceptional value 0, where the set consists of two entire functions of smaller orders. Moreover, the exact form of f is given and an example is provided to show the sharpness of the 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":"68266754","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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