In this paper, we apply the notion of B-summability to define a more general case of ideal convergence. We study several properties of this new summability method.
{"title":"IDEAL CONVERGENCE VIA REGULAR MATRIX SUMMABILTY METHOD","authors":"Osama H.H. EDELY, M. Mursaleen","doi":"10.54379/jiasf-2022-2-2","DOIUrl":"https://doi.org/10.54379/jiasf-2022-2-2","url":null,"abstract":"In this paper, we apply the notion of B-summability to define a more general case of ideal convergence. We study several properties of this new summability method.","PeriodicalId":43883,"journal":{"name":"Journal of Inequalities and Special Functions","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42060137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let λ > 0 and Φλ := {ϕ1,λ, ϕ2,λ, . . . } be the system of dilated Laguerre functions. We show that if L1 (R+) ∩ L∞(R+) is embedded into a separable Banach function space X(R+), then the linear span of Φλ is dense in X(R+). This implies that the linear span of Φλ is dense in every separable rearrangement-invariant space X(R+) and in every separable variable Lebesgue space Lp(·) (R+)
{"title":"ON THE DENSITY OF LAGUERRE FUNCTIONS IN SOME BANACH FUNCTION SPACES","authors":"C. Fernandes, Oleksiy Karlovych, M. A. Valente","doi":"10.54379/jiasf-2022-2-4","DOIUrl":"https://doi.org/10.54379/jiasf-2022-2-4","url":null,"abstract":"Let λ > 0 and Φλ := {ϕ1,λ, ϕ2,λ, . . . } be the system of dilated Laguerre functions. We show that if L1 (R+) ∩ L∞(R+) is embedded into a separable Banach function space X(R+), then the linear span of Φλ is dense in X(R+). This implies that the linear span of Φλ is dense in every separable rearrangement-invariant space X(R+) and in every separable variable Lebesgue space Lp(·) (R+)","PeriodicalId":43883,"journal":{"name":"Journal of Inequalities and Special Functions","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43111797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Huang et al in the paper [Some inequalities of the Hermite–Hadamard Type for k-fractional conformable integrals, The Australian Journal of Mathematical Analysis and Applications, 16 (2019), no. 7, pp. 1-9] proved some new Hermite–Hadamard type inequalities for k-fractional conformable integrals for convex functions. In this paper, we extend and generalize the main result of the above-mentioned paper for (k, r)-fractional conformable integrals for positive–convex stochastic process and also point out a mistake (omission) in ([6], Theorem 3.1). In addition, we prove a new Hermite–Hadamard type inequality for ψ-fractional conformable integrals for positive–convex stochastic process.
{"title":"NEW ψ - & (k, r)- FRACTIONAL CONFORMABLE INTEGRALS AND INEQUALITIES OF THE HERMITE–HADAMARD TYPE FOR POSITIVE–CONVEX STOCHASTIC PROCESSES","authors":"Mcsylvester EJIGHIKEME OMABA","doi":"10.54379/jiasf-2022-2-3","DOIUrl":"https://doi.org/10.54379/jiasf-2022-2-3","url":null,"abstract":"Huang et al in the paper [Some inequalities of the Hermite–Hadamard Type for k-fractional conformable integrals, The Australian Journal of Mathematical Analysis and Applications, 16 (2019), no. 7, pp. 1-9] proved some new Hermite–Hadamard type inequalities for k-fractional conformable integrals for convex functions. In this paper, we extend and generalize the main result of the above-mentioned paper for (k, r)-fractional conformable integrals for positive–convex stochastic process and also point out a mistake (omission) in ([6], Theorem 3.1). In addition, we prove a new Hermite–Hadamard type inequality for ψ-fractional conformable integrals for positive–convex stochastic process.","PeriodicalId":43883,"journal":{"name":"Journal of Inequalities and Special Functions","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49548490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, Reduced Differential Transform method in the framework of (p, q)-calculus, denoted by Rp,qDT , has been introduced and applied in solving a variety of differential equations such as diffusion equation, 2Dwave equation, K-dV equation, Burgers equations and Ito system. While the diffusion equation has been studied for the special case p = 1, i.e., in the framework of q-calculus, the other equations have not been studied even in q-calculus.
{"title":"Reduced $pq$-Differential Transform Method and Applications","authors":"P. Jain, C. Basu, V. Panwar","doi":"10.54379/jiasf-2022-1-3","DOIUrl":"https://doi.org/10.54379/jiasf-2022-1-3","url":null,"abstract":"In this paper, Reduced Differential Transform method in the framework of (p, q)-calculus, denoted by Rp,qDT , has been introduced and applied in solving a variety of differential equations such as diffusion equation, 2Dwave equation, K-dV equation, Burgers equations and Ito system. While the diffusion equation has been studied for the special case p = 1, i.e., in the framework of q-calculus, the other equations have not been studied even in q-calculus.","PeriodicalId":43883,"journal":{"name":"Journal of Inequalities and Special Functions","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48168226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we define fuzzy parameterized relative soft sets over some semigroups and give some its properties. Moreover, we construct a new algorithm for solving some decision-making problems based on fuzzy parameterized relative soft sets over some semigroups.
{"title":"Fuzzy parameterized relative soft sets over some semigroups in decision-making problems","authors":"Peerapong Suebsan","doi":"10.54379/jiasf-2022-1-2","DOIUrl":"https://doi.org/10.54379/jiasf-2022-1-2","url":null,"abstract":"In this paper, we define fuzzy parameterized relative soft sets over some semigroups and give some its properties. Moreover, we construct a new algorithm for solving some decision-making problems based on fuzzy parameterized relative soft sets over some semigroups.","PeriodicalId":43883,"journal":{"name":"Journal of Inequalities and Special Functions","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41836388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohd Shoaib Khan, Meenakshi Kaushal, Q. M. Danish Lohani
In machine learning, distance measure plays an important role in defining the similarity between two data-items. In the paper, we discuss some of the drawbacks of distance measures (metrics) with their possibly induced clustering algorithms. Further, to overcome the drawbacks, we propose a novel intuitionistic fuzzy distance measure associated with generalized cesa´ro paranormed sequence space Cesq p(F). We also discuss some geometric properties of Cesq p(F). Moreover, the proposed distance measure is utilized in k-mean clustering algorithm to propose fuzzy c-mean clustering algorithm for Cesq p(F)
{"title":"http://ilirias.com/jiasf/vol_13_issue_1.html","authors":"Mohd Shoaib Khan, Meenakshi Kaushal, Q. M. Danish Lohani","doi":"10.54379/jiasf-2022-1-1","DOIUrl":"https://doi.org/10.54379/jiasf-2022-1-1","url":null,"abstract":"In machine learning, distance measure plays an important role in defining the similarity between two data-items. In the paper, we discuss some of the drawbacks of distance measures (metrics) with their possibly induced clustering algorithms. Further, to overcome the drawbacks, we propose a novel intuitionistic fuzzy distance measure associated with generalized cesa´ro paranormed sequence space Cesq p(F). We also discuss some geometric properties of Cesq p(F). Moreover, the proposed distance measure is utilized in k-mean clustering algorithm to propose fuzzy c-mean clustering algorithm for Cesq p(F)","PeriodicalId":43883,"journal":{"name":"Journal of Inequalities and Special Functions","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46671179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Th purpose of this paper is to extend the Łojasiewicz inequality for functions definable in some subclass of P-minimal structures. More precisely, we prove that the Łojasiewicz inequality holds for functions definable in poptimal expansions of Qp. It is also shown that the Łojasiewicz exponent is a rational number in such p-optimal expansions.
{"title":"ŁOJASIEWICZ INEQUALITY IN P-MINIMAL STRUCTURES","authors":"A. Srhir","doi":"10.54379/jiasf-2021-4-2","DOIUrl":"https://doi.org/10.54379/jiasf-2021-4-2","url":null,"abstract":"Th purpose of this paper is to extend the Łojasiewicz inequality for functions definable in some subclass of P-minimal structures. More precisely, we prove that the Łojasiewicz inequality holds for functions definable in poptimal expansions of Qp. It is also shown that the Łojasiewicz exponent is a rational number in such p-optimal expansions.","PeriodicalId":43883,"journal":{"name":"Journal of Inequalities and Special Functions","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49331485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
By use of some non-negative Hermitian forms defined for n-tuple of bounded linear operators on the Hilbert space (H, h·, ·i) we establish new numerical radius and operator norm inequalities for sum of products of operators
{"title":"FURTHER INEQUALITIES FOR THE EUCLIDEAN OPERATOR RADIUS","authors":"H. Ranjbar, A. Niknam","doi":"10.54379/jiasf-2021-4-3","DOIUrl":"https://doi.org/10.54379/jiasf-2021-4-3","url":null,"abstract":"By use of some non-negative Hermitian forms defined for n-tuple of bounded linear operators on the Hilbert space (H, h·, ·i) we establish new numerical radius and operator norm inequalities for sum of products of operators","PeriodicalId":43883,"journal":{"name":"Journal of Inequalities and Special Functions","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49560893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce here the mixed generalized multivariate Prabhakar type left and right fractional integrals and study their basic properties, such as preservation of continuity and their boundedness as positive linear operators. Then we produce an interesting variety of related multivariate left and right fractional Hardy type inequalities under convexity. We introduce also other related multivariate fractional integrals
{"title":"GENERALIZED MULTIVARIATE PRABHAKAR TYPE FRACTIONAL INTEGRALS AND INEQUALITIES","authors":"George A. Anastassiou","doi":"10.54379/jiasf-2021-4-1","DOIUrl":"https://doi.org/10.54379/jiasf-2021-4-1","url":null,"abstract":"We introduce here the mixed generalized multivariate Prabhakar type left and right fractional integrals and study their basic properties, such as preservation of continuity and their boundedness as positive linear operators. Then we produce an interesting variety of related multivariate left and right fractional Hardy type inequalities under convexity. We introduce also other related multivariate fractional integrals","PeriodicalId":43883,"journal":{"name":"Journal of Inequalities and Special Functions","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48441129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We derive tail asymptotics for the running maximum of the CoxIngersoll-Ross process. The main result is proved by the saddle point method, where the tail estimate uses a new monotonicity property of the Kummer function. This auxiliary result is established by a computer algebra assisted proof. Moreover, we analyse the coefficients of the eigenfunction expansion of the running maximum distribution asymptotically.
{"title":"The running maximum of the Cox-Ingersoll-Ross process with some properties of the Kummer function","authors":"S. Gerhold, F. Hubalek, R. Paris","doi":"10.54379/jiasf-2022-2-1","DOIUrl":"https://doi.org/10.54379/jiasf-2022-2-1","url":null,"abstract":"We derive tail asymptotics for the running maximum of the CoxIngersoll-Ross process. The main result is proved by the saddle point method, where the tail estimate uses a new monotonicity property of the Kummer function. This auxiliary result is established by a computer algebra assisted proof. Moreover, we analyse the coefficients of the eigenfunction expansion of the running maximum distribution asymptotically.","PeriodicalId":43883,"journal":{"name":"Journal of Inequalities and Special Functions","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41458086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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