Abstract The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called ( κ , n {kappa,n} )-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a ( κ , n ) {(kappa,n)} -Fourier multiplier theorem for L 2 {L^{2}} Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m. This allows us to establish the analogue of the Boas-type result for ℱ κ , n {mathcal{F}_{kappa,n}} .
摘要 本文旨在证明 Titchmarsh 定理对广义傅里叶变换 ( κ , n {kappa,n} )-Fourier 变换的推广，其中 n 为正整数，κ 为来自 Dunkl 理论的常数。作为应用，我们推导出 L 2 {L^{2}} 的 ( κ , n ) {(kappa,n)} - 傅立叶乘数定理。Lipschitz 空间的傅里叶乘数定理。此外，我们给出了必要条件，以确保 f 属于阶数为 m 的广义 Lipschitz 类中的任意一类。这使得我们可以为 ℱ κ , n {mathcal{F}_{kappa,n}} 建立类似的 Boas 型结果。.
{"title":"Titchmarsh and Boas-type theorems related to (κ,n)-Fourier transform","authors":"Mehrez Mannai, S. Negzaoui","doi":"10.1515/anly-2023-0045","DOIUrl":"https://doi.org/10.1515/anly-2023-0045","url":null,"abstract":"Abstract The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called ( κ , n {kappa,n} )-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a ( κ , n ) {(kappa,n)} -Fourier multiplier theorem for L 2 {L^{2}} Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m. This allows us to establish the analogue of the Boas-type result for ℱ κ , n {mathcal{F}_{kappa,n}} .","PeriodicalId":47773,"journal":{"name":"ANALYSIS","volume":"39 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139123267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called ( κ , n {kappa,n} )-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a ( κ , n ) {(kappa,n)} -Fourier multiplier theorem for L 2 {L^{2}} Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m. This allows us to establish the analogue of the Boas-type result for ℱ κ , n {mathcal{F}_{kappa,n}} .
摘要 本文旨在证明 Titchmarsh 定理对广义傅里叶变换 ( κ , n {kappa,n} )-Fourier 变换的推广，其中 n 为正整数，κ 为来自 Dunkl 理论的常数。作为应用，我们推导出 L 2 {L^{2}} 的 ( κ , n ) {(kappa,n)} - 傅立叶乘数定理。Lipschitz 空间的傅里叶乘数定理。此外，我们给出了必要条件，以确保 f 属于阶数为 m 的广义 Lipschitz 类中的任意一类。这使得我们可以为 ℱ κ , n {mathcal{F}_{kappa,n}} 建立类似的 Boas 型结果。.
{"title":"Titchmarsh and Boas-type theorems related to (κ,n)-Fourier transform","authors":"Mehrez Mannai, S. Negzaoui","doi":"10.1515/anly-2023-0045","DOIUrl":"https://doi.org/10.1515/anly-2023-0045","url":null,"abstract":"Abstract The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called ( κ , n {kappa,n} )-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a ( κ , n ) {(kappa,n)} -Fourier multiplier theorem for L 2 {L^{2}} Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m. This allows us to establish the analogue of the Boas-type result for ℱ κ , n {mathcal{F}_{kappa,n}} .","PeriodicalId":47773,"journal":{"name":"ANALYSIS","volume":"39 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139123611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ashish Verma, K. Yadav, Bhagwat Sharan, D.L. Suthar
Abstract In this paper, we investigate the matrix analogues of the Ψ-beta and Ψ-gamma functions, as well as their properties. With the help of the Ψ-beta matrix function (BMF), we introduce the Ψ-Gauss hypergeometric matrix function (GHMF) and the Ψ-Kummer hypergeometric matrix function (KHMF) and derive certain properties for these matrix functions. Finally, the Ψ-Appell and the Ψ-Lauricella matrix functions are defined by applications of the Ψ-BMF, and their integral representations are also given.
{"title":"Some properties of Ψ-gamma, Ψ-beta and Ψ-hypergeometric matrix functions","authors":"Ashish Verma, K. Yadav, Bhagwat Sharan, D.L. Suthar","doi":"10.1515/anly-2023-0068","DOIUrl":"https://doi.org/10.1515/anly-2023-0068","url":null,"abstract":"Abstract In this paper, we investigate the matrix analogues of the Ψ-beta and Ψ-gamma functions, as well as their properties. With the help of the Ψ-beta matrix function (BMF), we introduce the Ψ-Gauss hypergeometric matrix function (GHMF) and the Ψ-Kummer hypergeometric matrix function (KHMF) and derive certain properties for these matrix functions. Finally, the Ψ-Appell and the Ψ-Lauricella matrix functions are defined by applications of the Ψ-BMF, and their integral representations are also given.","PeriodicalId":47773,"journal":{"name":"ANALYSIS","volume":"39 7","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139123700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
H. Abass, O. Oyewole, Olayinka Martins Onifade, O. Narain
Abstract In this paper, our main interest is to propose a viscosity iterative method for approximating solutions of variational inequality problems, resolvents of monotone operators and fixed points of ρ-demimetric mappings with multiple output sets in Hadamard spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. Also, we present an application of our main result to a convex minimization problem. Our results improve and generalize many related results in the literature.
{"title":"Iterative approximation of common solution of variational inequality and certain optimization problems with multiple output sets in Hadamard space","authors":"H. Abass, O. Oyewole, Olayinka Martins Onifade, O. Narain","doi":"10.1515/anly-2022-1075","DOIUrl":"https://doi.org/10.1515/anly-2022-1075","url":null,"abstract":"Abstract In this paper, our main interest is to propose a viscosity iterative method for approximating solutions of variational inequality problems, resolvents of monotone operators and fixed points of ρ-demimetric mappings with multiple output sets in Hadamard spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. Also, we present an application of our main result to a convex minimization problem. Our results improve and generalize many related results in the literature.","PeriodicalId":47773,"journal":{"name":"ANALYSIS","volume":"47 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139123862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This research paper aims to introduce the concept of lacunary ideal Cauchy sequences of fuzzy variables in a credibility space. We establish the interrelationships between this notion with lacunary ideal convergent sequences in the same structure from several aspects of credibility. Furthermore, we explore the concepts of strongly lacunary Cauchy, strongly ℐ {mathcal{I}} -lacunary Cauchy, and strongly ℐ ∗ {mathcal{I}^{ast}} -lacunary Cauchy sequences of fuzzy variables within the context of credibility. We also examine the interconnections between these concepts and analyze their relationships.
{"title":"Characterization of lacunary ℐ-convergent sequences in credibility space","authors":"Mousami Das, Ömer Kişi, B. Tripathy, Birojit Das","doi":"10.1515/anly-2023-0084","DOIUrl":"https://doi.org/10.1515/anly-2023-0084","url":null,"abstract":"Abstract This research paper aims to introduce the concept of lacunary ideal Cauchy sequences of fuzzy variables in a credibility space. We establish the interrelationships between this notion with lacunary ideal convergent sequences in the same structure from several aspects of credibility. Furthermore, we explore the concepts of strongly lacunary Cauchy, strongly ℐ {mathcal{I}} -lacunary Cauchy, and strongly ℐ ∗ {mathcal{I}^{ast}} -lacunary Cauchy sequences of fuzzy variables within the context of credibility. We also examine the interconnections between these concepts and analyze their relationships.","PeriodicalId":47773,"journal":{"name":"ANALYSIS","volume":"27 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139123955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
H. Abass, O. Oyewole, Olayinka Martins Onifade, O. Narain
Abstract In this paper, our main interest is to propose a viscosity iterative method for approximating solutions of variational inequality problems, resolvents of monotone operators and fixed points of ρ-demimetric mappings with multiple output sets in Hadamard spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. Also, we present an application of our main result to a convex minimization problem. Our results improve and generalize many related results in the literature.
{"title":"Iterative approximation of common solution of variational inequality and certain optimization problems with multiple output sets in Hadamard space","authors":"H. Abass, O. Oyewole, Olayinka Martins Onifade, O. Narain","doi":"10.1515/anly-2022-1075","DOIUrl":"https://doi.org/10.1515/anly-2022-1075","url":null,"abstract":"Abstract In this paper, our main interest is to propose a viscosity iterative method for approximating solutions of variational inequality problems, resolvents of monotone operators and fixed points of ρ-demimetric mappings with multiple output sets in Hadamard spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. Also, we present an application of our main result to a convex minimization problem. Our results improve and generalize many related results in the literature.","PeriodicalId":47773,"journal":{"name":"ANALYSIS","volume":"47 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139124225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called ( κ , n {kappa,n} )-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a ( κ , n ) {(kappa,n)} -Fourier multiplier theorem for L 2 {L^{2}} Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m. This allows us to establish the analogue of the Boas-type result for ℱ κ , n {mathcal{F}_{kappa,n}} .
摘要 本文旨在证明 Titchmarsh 定理对广义傅里叶变换 ( κ , n {kappa,n} )-Fourier 变换的推广，其中 n 为正整数，κ 为来自 Dunkl 理论的常数。作为应用，我们推导出 L 2 {L^{2}} 的 ( κ , n ) {(kappa,n)} - 傅立叶乘数定理。Lipschitz 空间的傅里叶乘数定理。此外，我们给出了必要条件，以确保 f 属于阶数为 m 的广义 Lipschitz 类中的任意一类。这使得我们可以为 ℱ κ , n {mathcal{F}_{kappa,n}} 建立类似的 Boas 型结果。.
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Abstract The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called ( κ , n {kappa,n} )-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a ( κ , n ) {(kappa,n)} -Fourier multiplier theorem for L 2 {L^{2}} Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m. This allows us to establish the analogue of the Boas-type result for ℱ κ , n {mathcal{F}_{kappa,n}} .
摘要 本文旨在证明 Titchmarsh 定理对广义傅里叶变换 ( κ , n {kappa,n} )-Fourier 变换的推广，其中 n 为正整数，κ 为来自 Dunkl 理论的常数。作为应用，我们推导出 L 2 {L^{2}} 的 ( κ , n ) {(kappa,n)} - 傅立叶乘数定理。Lipschitz 空间的傅里叶乘数定理。此外，我们给出了必要条件，以确保 f 属于阶数为 m 的广义 Lipschitz 类中的任意一类。这使得我们可以为 ℱ κ , n {mathcal{F}_{kappa,n}} 建立类似的 Boas 型结果。.
{"title":"Titchmarsh and Boas-type theorems related to (κ,n)-Fourier transform","authors":"Mehrez Mannai, S. Negzaoui","doi":"10.1515/anly-2023-0045","DOIUrl":"https://doi.org/10.1515/anly-2023-0045","url":null,"abstract":"Abstract The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called ( κ , n {kappa,n} )-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a ( κ , n ) {(kappa,n)} -Fourier multiplier theorem for L 2 {L^{2}} Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m. This allows us to establish the analogue of the Boas-type result for ℱ κ , n {mathcal{F}_{kappa,n}} .","PeriodicalId":47773,"journal":{"name":"ANALYSIS","volume":"39 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139112690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ashish Verma, K. Yadav, Bhagwat Sharan, D.L. Suthar
Abstract In this paper, we investigate the matrix analogues of the Ψ-beta and Ψ-gamma functions, as well as their properties. With the help of the Ψ-beta matrix function (BMF), we introduce the Ψ-Gauss hypergeometric matrix function (GHMF) and the Ψ-Kummer hypergeometric matrix function (KHMF) and derive certain properties for these matrix functions. Finally, the Ψ-Appell and the Ψ-Lauricella matrix functions are defined by applications of the Ψ-BMF, and their integral representations are also given.
{"title":"Some properties of Ψ-gamma, Ψ-beta and Ψ-hypergeometric matrix functions","authors":"Ashish Verma, K. Yadav, Bhagwat Sharan, D.L. Suthar","doi":"10.1515/anly-2023-0068","DOIUrl":"https://doi.org/10.1515/anly-2023-0068","url":null,"abstract":"Abstract In this paper, we investigate the matrix analogues of the Ψ-beta and Ψ-gamma functions, as well as their properties. With the help of the Ψ-beta matrix function (BMF), we introduce the Ψ-Gauss hypergeometric matrix function (GHMF) and the Ψ-Kummer hypergeometric matrix function (KHMF) and derive certain properties for these matrix functions. Finally, the Ψ-Appell and the Ψ-Lauricella matrix functions are defined by applications of the Ψ-BMF, and their integral representations are also given.","PeriodicalId":47773,"journal":{"name":"ANALYSIS","volume":"39 7","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139113223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called ( κ , n {kappa,n} )-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a ( κ , n ) {(kappa,n)} -Fourier multiplier theorem for L 2 {L^{2}} Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m. This allows us to establish the analogue of the Boas-type result for ℱ κ , n {mathcal{F}_{kappa,n}} .
摘要 本文旨在证明 Titchmarsh 定理对广义傅里叶变换 ( κ , n {kappa,n} )-Fourier 变换的推广，其中 n 为正整数，κ 为来自 Dunkl 理论的常数。作为应用，我们推导出 L 2 {L^{2}} 的 ( κ , n ) {(kappa,n)} - 傅立叶乘数定理。Lipschitz 空间的傅里叶乘数定理。此外，我们给出了必要条件，以确保 f 属于阶数为 m 的广义 Lipschitz 类中的任意一类。这使得我们可以为 ℱ κ , n {mathcal{F}_{kappa,n}} 建立类似的 Boas 型结果。.
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