In this article, we study a system of viscoelastic parabolic type Kirchhoff equation with multiple nonlinearities. We obtain a finite time blow up of solutions and exponential growth of solution with negative initial energy.
{"title":"Blow up and growth of solutions to a viscoelastic parabolic type Kirchhoff equation","authors":"E. Pişkin, F. Ekinci","doi":"10.2298/fil2302519p","DOIUrl":"https://doi.org/10.2298/fil2302519p","url":null,"abstract":"In this article, we study a system of viscoelastic parabolic type Kirchhoff equation with multiple nonlinearities. We obtain a finite time blow up of solutions and exponential growth of solution with negative initial energy.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68267596","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":"1 1","pages":""},"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}
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":"1 1","pages":""},"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":"1 1","pages":""},"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}
Let A be a Banach algebra with a bounded approximate identity bounded by 1. Two new topologies ?so and ?wo are introduced on A. We study these topologies and compare them with each other and with the norm topology. The properties of ?so and ?wo are then studied further and we pay attention to the group algebra L1(G) of a locally compact group G. Various necessary and sufficient conditions are found for a locally compact group G to be finite.
{"title":"Induced topologies on certain Banach algebras","authors":"M. Eshaghi, A. Ghaffari, M. Sahabi","doi":"10.2298/fil2304311e","DOIUrl":"https://doi.org/10.2298/fil2304311e","url":null,"abstract":"Let A be a Banach algebra with a bounded approximate identity bounded by 1. Two new topologies ?so and ?wo are introduced on A. We study these topologies and compare them with each other and with the norm topology. The properties of ?so and ?wo are then studied further and we pay attention to the group algebra L1(G) of a locally compact group G. Various necessary and sufficient conditions are found for a locally compact group G to be finite.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"47 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68269023","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 present paper we prove a fixed point theorem for a one parameter family of contractive self-mappings, of a complete metric space or a complete b-metric space, each member of which has a unique fixed point that is also the unique common fixed point of the family; the mappings may be continuous or discontinuous at the fixed point. We also prove that under the assumption of a weaker form of continuity the fixed point property for mappings satisfying the contractive conditions employed by us implies completeness of the underlying space. The characterization of completeness obtained by us not only contains Subrahmanyam?s theorem on characterization of completeness as a particular case but also extends it to b-metric spaces. Results on contractive mappings with discontinuity at the fixed point have found applications in neural networks with discontinuous activation function (e.g. Ozgur and Tas [19, 20]).
{"title":"Fixed points of a family of mappings and equivalent characterizations","authors":"Abhijit Pant, R. Pant, M. Joshi, V. Rakočević","doi":"10.2298/fil2305391p","DOIUrl":"https://doi.org/10.2298/fil2305391p","url":null,"abstract":"In the present paper we prove a fixed point theorem for a one parameter family of contractive self-mappings, of a complete metric space or a complete b-metric space, each member of which has a unique fixed point that is also the unique common fixed point of the family; the mappings may be continuous or discontinuous at the fixed point. We also prove that under the assumption of a weaker form of continuity the fixed point property for mappings satisfying the contractive conditions employed by us implies completeness of the underlying space. The characterization of completeness obtained by us not only contains Subrahmanyam?s theorem on characterization of completeness as a particular case but also extends it to b-metric spaces. Results on contractive mappings with discontinuity at the fixed point have found applications in neural networks with discontinuous activation function (e.g. Ozgur and Tas [19, 20]).","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68269265","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":"1 1","pages":""},"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}
We consider in this paper a hyperbolic quasilinear version of the Navier-Stokes equations in three space dimensions, obtained by using Cattaneo type law instead of a Fourier law. In our earlier work [2], we proved the global existence and uniqueness of solutions for initial data small enough in the space H4(R3)3 ? H3(R3)3. In this paper, we refine our previous result in [2], we establish the existence under a significantly lower regularity. We first prove the local existence and uniqueness of solution, for initial data in the space H5 2 +?(R3)3 ?H32 +?(R3)3, ? > 0. Under weaker smallness assumptions on the initial data and the forcing term, we prove the global existence of solutions. Finally, we show that if ? is close to 0, then the solution of the perturbed equation is close to the solution of the classical Navier-Stokes equations.
{"title":"Hyperbolic Navier-Stokes equations in three space dimensions","authors":"Bouthaina Abdelhedi","doi":"10.2298/fil2307209a","DOIUrl":"https://doi.org/10.2298/fil2307209a","url":null,"abstract":"We consider in this paper a hyperbolic quasilinear version of the Navier-Stokes equations in three space dimensions, obtained by using Cattaneo type law instead of a Fourier law. In our earlier work [2], we proved the global existence and uniqueness of solutions for initial data small enough in the space H4(R3)3 ? H3(R3)3. In this paper, we refine our previous result in [2], we establish the existence under a significantly lower regularity. We first prove the local existence and uniqueness of solution, for initial data in the space H5 2 +?(R3)3 ?H32 +?(R3)3, ? > 0. Under weaker smallness assumptions on the initial data and the forcing term, we prove the global existence of solutions. Finally, we show that if ? is close to 0, then the solution of the perturbed equation is close to the solution of the classical Navier-Stokes equations.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68272476","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":"1 1","pages":""},"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}
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":"1 1","pages":""},"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}
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