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 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":"16 1","pages":""},"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}
A number of properties for the classes Bp-1 and B*p have been proved. The class Bp-1 characterizes the Lp- inequality involving the averaging operator and the class B*p characterizes the Lp-inequality involving the adjoint averaging operator. The reverse inequalities involving the integral operators in Lp? have also been studied.
{"title":"Integral operators on grand Lebesgue spaces and related weights with properties","authors":"Santosh Kaushik, T. Khan, H. Chaudhary","doi":"10.2298/fil2306767k","DOIUrl":"https://doi.org/10.2298/fil2306767k","url":null,"abstract":"A number of properties for the classes Bp-1 and B*p have been proved. The class Bp-1 characterizes the Lp- inequality involving the averaging operator and the class B*p characterizes the Lp-inequality involving the adjoint averaging operator. The reverse inequalities involving the integral operators in Lp? have also been studied.","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":"68270880","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 study the Neumann problem with Leray-Lions type operator. Using the classical variational theory, we prove the existence, uniqueness and multiplicity of solutions. As far as we know, this is the first attempt to investigate such a fourth-order problem involving Leray-Lions type operators.
{"title":"On a fourth-order Neumann problem in variable exponent spaces","authors":"J. Zuo, A. El, S. Taarabti, Dušan D. Repovš","doi":"10.2298/fil2307027z","DOIUrl":"https://doi.org/10.2298/fil2307027z","url":null,"abstract":"We study the Neumann problem with Leray-Lions type operator. Using the classical variational theory, we prove the existence, uniqueness and multiplicity of solutions. As far as we know, this is the first attempt to investigate such a fourth-order problem involving Leray-Lions type operators.","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":"68271558","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 the asymptotic expressions of the scaled value function and the optimal redemption boundary of stock loan with dividend-paying near maturity. Using the equation satisfied by the derivative of the value function at the exercise boundary, we set up the asymptotic expression for the boundary. When the risk-free rate r is smaller than the loan rate ?, i.e., r < ?, the boundary tends to Ke?T0 in parabolic-logarithm form, this case is the main result. For the case r ? ?, the corresponding problem returns back to a usual American call option with interest-free rate r ? ? and the existing results can be utilized to make proper adjustments for the stock loan. The matched expansion for the value function is performed with a small parameter. Numerical examples are provided to demonstrate the effectiveness of the proposed method.
{"title":"Asymptotic analysis for stock loans near maturity","authors":"Yongqing Xu","doi":"10.2298/fil2307105x","DOIUrl":"https://doi.org/10.2298/fil2307105x","url":null,"abstract":"In this paper, we derive the asymptotic expressions of the scaled value function and the optimal redemption boundary of stock loan with dividend-paying near maturity. Using the equation satisfied by the derivative of the value function at the exercise boundary, we set up the asymptotic expression for the boundary. When the risk-free rate r is smaller than the loan rate ?, i.e., r < ?, the boundary tends to Ke?T0 in parabolic-logarithm form, this case is the main result. For the case r ? ?, the corresponding problem returns back to a usual American call option with interest-free rate r ? ? and the existing results can be utilized to make proper adjustments for the stock loan. The matched expansion for the value function is performed with a small parameter. Numerical examples are provided to demonstrate the effectiveness of the proposed method.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"94 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68271808","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}
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":"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":"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 studies the exponential stability result is derived for the second-order fractional stochastic integro-differential equations (FSIDEs) driven by sub-fractional Brownian motion (sub-fBm). By constructing a successive approximation method, we present pth moment exponential stability result of second-order FSIDEs using stochastic analysis techniques and fractional calculus (FC). At last, an example is demonstrated to illustrate the obtained theoretical result.
{"title":"Exponential stability of second-order fractional stochastic integro-differential equations","authors":"K. Dhanalakshmi, P. Balasubramaniam","doi":"10.2298/fil2309699d","DOIUrl":"https://doi.org/10.2298/fil2309699d","url":null,"abstract":"In this paper studies the exponential stability result is derived for the second-order fractional stochastic integro-differential equations (FSIDEs) driven by sub-fractional Brownian motion (sub-fBm). By constructing a successive approximation method, we present pth moment exponential stability result of second-order FSIDEs using stochastic analysis techniques and fractional calculus (FC). At last, an example is demonstrated to illustrate the obtained theoretical result.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135595644","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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