Given Banach algebras $A$, $B$ and a continuous homomorphism $theta:Blongrightarrow A$ with $VertthetaVert leq1$, we obtain characterization of spectrum, homomorphisms and multipliers of $Atimes_{theta}B$, which is a strongly splitting Banach algebra extension of $B$ by $A$. Also we characterize the semisimplicity of these algebras.
{"title":"Spectrum, homomorphisms and multipliers of Lau product of Banach algebras","authors":"M. Valaei̇, A. Zivari-kazempour","doi":"10.15672/hujms.1287866","DOIUrl":"https://doi.org/10.15672/hujms.1287866","url":null,"abstract":"Given Banach algebras $A$, $B$ and a continuous homomorphism $theta:Blongrightarrow A$ with $VertthetaVert leq1$, we obtain characterization of spectrum, homomorphisms and multipliers of $Atimes_{theta}B$, which is a strongly splitting Banach algebra extension of $B$ by $A$. Also we characterize the semisimplicity of these algebras.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"8 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439504","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}
The Riemann-Liouville operator has been extensively investigated and has witnessed a remarkable development in numerous fields of harmonic analysis. In this paper, we consider the Stockwell transform associated with the Riemann-Liouville operator. Knowing the fact that the study of the time-frequency analysis are both theoretically interesting and practically useful, we investigated several problems for this subject on the setting of this generalized Stockwell transform. Firstly, we explore the Shapiro uncertainty principle for this transform. Next, we study the boundedness and compactness of localization operators associated with the generalized Stockwell transforms. Finally, the scalogram for the generalized Stockwell transform are introduced and studied at the end.
{"title":"TIME-FREQUENCY ANALYSIS ASSOCIATED WITH THE GENERALIZED STOCKWELL TRANSFORM","authors":"Nadia Ben Hamadi, Zineb Hafirassou, H. Mejjaoli","doi":"10.15672/hujms.1198408","DOIUrl":"https://doi.org/10.15672/hujms.1198408","url":null,"abstract":"The Riemann-Liouville operator has been extensively investigated and has witnessed a remarkable development in numerous fields of harmonic analysis. \u0000In this paper, we consider the Stockwell transform associated with the Riemann-Liouville operator. \u0000Knowing the fact that the study of the time-frequency analysis are both theoretically \u0000interesting and practically useful, we investigated several problems for this subject on the setting of this generalized Stockwell transform. Firstly, we explore the Shapiro uncertainty principle for this transform. Next, we study the boundedness and compactness of localization operators associated with the generalized Stockwell transforms. \u0000Finally, the scalogram for the generalized Stockwell transform are introduced and studied at the end.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"3 9","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439919","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 light of the well-established and widely-used theory of differential subordination, recent works incorporating fuzzy elements into Geometric Function Theory have given rise to the concept of fuzzy differential subordination. Second-order fuzzy differential subordinations were taken into consideration for studies up until this point. The research described in this paper aims to expand the concept of fuzzy differential subordination to third-order fuzzy differential subordination, building on an idea first put forth in 2011 by José A. Antonino and Sanford S. Miller and still being investigated by scholars today. The key concepts and preliminary findings required for the development of this branch of fuzzy differential subordination are introduced. The class of admissible functions is specified, the fundamental theorems are established and the fundamental concepts of the third-order fuzzy subordination approach are presented. The example given demonstrates the applicability of the new findings.
鉴于微分从属性理论已得到广泛应用，最近将模糊元素纳入几何函数论的工作产生了模糊微分从属性的概念。在此之前的研究考虑的是二阶模糊微分从属关系。本文所述的研究旨在将模糊微分从属关系的概念扩展到三阶模糊微分从属关系，其基础是何塞-A-安东尼诺（José A. Antonino）和桑福德-S-米勒（Sanford S. Miller）于 2011 年首次提出的、至今仍有学者在研究的观点。本文介绍了发展模糊微分从属性这一分支所需的关键概念和初步发现。具体说明了可容许函数的类别，建立了基本定理，并介绍了三阶模糊从属关系方法的基本概念。所举实例证明了新发现的适用性。
{"title":"Introduction in third-order fuzzy differential subordination","authors":"G. Oros, G. Oros, Özlem Güney","doi":"10.15672/hujms.1319541","DOIUrl":"https://doi.org/10.15672/hujms.1319541","url":null,"abstract":"In light of the well-established and widely-used theory of differential subordination, recent works incorporating fuzzy elements into Geometric Function Theory have given rise to the concept of fuzzy differential subordination. Second-order fuzzy differential subordinations were taken into consideration for studies up until this point. The research described in this paper aims to expand the concept of fuzzy differential subordination to third-order fuzzy differential subordination, building on an idea first put forth in 2011 by José A. Antonino and Sanford S. Miller and still being investigated by scholars today. The key concepts and preliminary findings required for the development of this branch of fuzzy differential subordination are introduced. The class of admissible functions is specified, the fundamental theorems are established and the fundamental concepts of the third-order fuzzy subordination approach are presented. The example given demonstrates the applicability of the new findings.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"69 24","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440786","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}
Z. M. M. M. Sayed, M. Adil Khan, Shahid Khan, J. Pečarić
This article is dedicated to a refinement of the classical Jensen inequality by virtue of some finite real sequences. Inequalities for various means are obtained from this refinement. Also, from the proposed refinement, the authors acquired some inequalities for Csisz^{a}r $Psi$- divergence and for Shannon and Zipf-Mandelbrot entropies. The refinement is further generalized through several finite real sequences.
{"title":"Refinement of the classical Jensen inequality using finite sequences","authors":"Z. M. M. M. Sayed, M. Adil Khan, Shahid Khan, J. Pečarić","doi":"10.15672/hujms.1270585","DOIUrl":"https://doi.org/10.15672/hujms.1270585","url":null,"abstract":"This article is dedicated to a refinement of the classical Jensen inequality by virtue of some finite real sequences. Inequalities for various means are obtained from this refinement. Also, from the proposed refinement, the authors acquired some inequalities for Csisz^{a}r $Psi$- divergence and for Shannon and Zipf-Mandelbrot entropies. The refinement is further generalized through several finite real sequences.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"63 7","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139441226","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 study, some properties for the pencils of singular Sturm-Liouville operators are investigated. Firstly, the behaviors of eigenvalues were learned, then the solutions of the inverse problem were given to determine the potential function and parameters of the boundary condition with the help of a dense set of nodal points and lastly we obtain a constructive solution to the inverse problems of this class.
{"title":"SPECTRAL PROPERTIES AND INVERSE NODAL PROBLEMS FOR SINGULAR DIFFUSION EQUATION","authors":"R. Ami̇rov, Sevim Durak","doi":"10.15672/hujms.1254445","DOIUrl":"https://doi.org/10.15672/hujms.1254445","url":null,"abstract":"In this study, some properties for the pencils of singular Sturm-Liouville operators are investigated. Firstly, the behaviors of eigenvalues were learned, then the solutions of the inverse problem were given to determine the potential function and parameters of the boundary condition with the help of a dense set of nodal points and lastly we obtain a constructive solution to the inverse problems of this class.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"88 5","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440505","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 are concerned with an inverse source Cauchy weighted problem involving a one-dimensional diffusion equation involving a time-fractional Riemann-Liouville derivative with 0
{"title":"An inverse source Cauchy-weighted time-fractional diffusion problem","authors":"R. Atmani̇a, Loubna Settara","doi":"10.15672/hujms.1230169","DOIUrl":"https://doi.org/10.15672/hujms.1230169","url":null,"abstract":"In the present paper, we are concerned with an inverse source Cauchy weighted problem involving a one-dimensional diffusion equation involving a time-fractional Riemann-Liouville derivative with 0","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"56 14","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139441068","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 focus on investigating the existence and approximation of periodic solutions for a nonlinear integro-differential system with a piecewise alternately advanced and retarded argument of generalized type, referred to as DEPCAG. The argument is a general step function, and we obtain criteria for the existence of periodic solutions for such equations. Our approach involves converting the given DEPCAG into an equivalent integral equation and using a new approach for periodic solutions. We construct appropriate mappings and employ a numerical-analytic method to investigate periodic solutions of the ordinary differential equation given by A. M. Samoilenko. Additionally, we use the contraction mapping principle to demonstrate the existence of a unique periodic solution.
在本文中，我们重点研究了一个非线性整微分方程的周期解的存在性和近似性，该非线性整微分方程具有片断交替前进和后退的广义参数，简称为 DEPCAG。参数是一般阶跃函数，我们得到了此类方程周期解存在的标准。我们的方法包括将给定的 DEPCAG 转换为等价积分方程，并使用新方法求周期解。我们构建了适当的映射，并采用数值分析方法研究了 A. M. Samoilenko 所给常微分方程的周期解。此外，我们还利用收缩映射原理证明了唯一周期解的存在。
{"title":"Numerical-analytic successive approximation method for the investigation of periodic solutions of nonlinear integro-differential systems with piecewise constant argument of generalized type","authors":"Kuo-shou Chi̇u","doi":"10.15672/hujms.1298168","DOIUrl":"https://doi.org/10.15672/hujms.1298168","url":null,"abstract":"In this paper, we focus on investigating the existence and approximation of periodic solutions for a nonlinear integro-differential system with a piecewise alternately advanced and retarded argument of generalized type, referred to as DEPCAG. The argument is a general step function, and we obtain criteria for the existence of periodic solutions for such equations. \u0000Our approach involves converting the given DEPCAG into an equivalent integral equation and using a new approach for periodic solutions. We construct appropriate mappings and employ a numerical-analytic method to investigate periodic solutions of the ordinary differential equation given by A. M. Samoilenko. \u0000Additionally, we use the contraction mapping principle to demonstrate the existence of a unique periodic solution.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"62 14","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139441262","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}
Fatma Çi̇ftci̇, Buğra Saraçoğlu, Neriman Akdam, Y. Akdoğan
In this study, the stress-strength reliability, R = P(Y < X) where Y represents the stress of a component and X represents this component’s strength, is obtained when X and Y have two independents generalized Gompertz distribution with different shape parameters under progressive type-II censoring. The Bayes and maximum likelihood estimators of stress-strength reliability can not be acquired in closed forms. The approximate Bayes estimators under squared error loss function by using Lindley’s approximations for stressstrength reliability are derived. A Monte Carlo simulation study is done to check performances of the approximate Bayes against performances of maximum likelihood estimators and observe the coverage probabilities and the intervals’ average width. In addition, the coverage probabilities of the parametric bootstrap estimates are calculated. Two applications based on real datasets are provided.
{"title":"Estimation of stress-strength reliability for generalized Gompertz distribution under progressive type-II censoring","authors":"Fatma Çi̇ftci̇, Buğra Saraçoğlu, Neriman Akdam, Y. Akdoğan","doi":"10.15672/hujms.961868","DOIUrl":"https://doi.org/10.15672/hujms.961868","url":null,"abstract":"In this study, the stress-strength reliability, R = P(Y < X) where Y represents the stress of a component and X represents this component’s strength, is obtained when X and Y have two independents generalized Gompertz distribution with different shape parameters under progressive type-II censoring. The Bayes and maximum likelihood estimators of stress-strength reliability can not be acquired in closed forms. The approximate Bayes estimators under squared error loss function by using Lindley’s approximations for stressstrength reliability are derived. A Monte Carlo simulation study is done to check performances of the approximate Bayes against performances of maximum likelihood estimators and observe the coverage probabilities and the intervals’ average width. In addition, the coverage probabilities of the parametric bootstrap estimates are calculated. Two applications based on real datasets are provided.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"514 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77355605","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 study, a discrete-time prey-predator model based on the Allee effect is presented. We examine the parametric conditions for local asymptotic stability of fixed points of this model. Furthermore, with the use of the center manifold theorem and bifurcation theory, we analyze the existence and directions of period-doubling and Neimark-Sacker bifurcations. The plots of maximum Lyapunov exponents provide indications of complexity and chaotic behavior. The feedback control approach is presented to stabilize the unstable fixed point. Numerical simulations are performed to support theoretical results.
{"title":"Bifurcation analysis and chaos control of discrete-time prey-predator model with Allee effect","authors":"Özlem AK GÜMÜŞ","doi":"10.15672/hujms.1179682","DOIUrl":"https://doi.org/10.15672/hujms.1179682","url":null,"abstract":"In this study, a discrete-time prey-predator model based on the Allee effect is presented. We examine the parametric conditions for local asymptotic stability of fixed points of this model. Furthermore, with the use of the center manifold theorem and bifurcation theory, we analyze the existence and directions of period-doubling and Neimark-Sacker bifurcations. The plots of maximum Lyapunov exponents provide indications of complexity and chaotic behavior. The feedback control approach is presented to stabilize the unstable fixed point. Numerical simulations are performed to support theoretical results.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"408 19","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72448267","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}
Amir Hamzeh KHAMMAR, Seyyed Mahdi AMİR JAHANSHAHİ, Hassan ZAREİ
The cumulative residual extropy is an uncertainty measure that parallels extropy in an absolutely continuous cumulative distribution function. The dynamic version of this measure is known as dynamic survival extropy. In this paper, we study some properties of the dynamic survival extropy using quantile function approach. Unlike the dynamic survival extropy, the quantile-based dynamic survival extropy determines the quantile density function uniquely through a simple relationship. We also extend the definition of quantile-based dynamic survival extropy into order statistics. Finally, an application of new quantile-based uncertainty measure as a risk measure is derived.
{"title":"On Quantile-Based Dynamic Survival Extropy and its Applications","authors":"Amir Hamzeh KHAMMAR, Seyyed Mahdi AMİR JAHANSHAHİ, Hassan ZAREİ","doi":"10.15672/hujms.823331","DOIUrl":"https://doi.org/10.15672/hujms.823331","url":null,"abstract":"The cumulative residual extropy is an uncertainty measure that parallels extropy in an absolutely continuous cumulative distribution function. The dynamic version of this measure is known as dynamic survival extropy. In this paper, we study some properties of the dynamic survival extropy using quantile function approach. Unlike the dynamic survival extropy, the quantile-based dynamic survival extropy determines the quantile density function uniquely through a simple relationship. We also extend the definition of quantile-based dynamic survival extropy into order statistics. Finally, an application of new quantile-based uncertainty measure as a risk measure is derived.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"24 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135768996","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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