An upper bound on a linear functional satisfying several constraints is found, then used to provide a short and simple proof of convergence, for orthogonal polynomial expansions. Mathematics subject classification (2010): 42C10, 26D20.
{"title":"Upper bounds for a general linear functional with application to orthogonal polynomial expansions","authors":"A. Mercer, P. R. Mercer","doi":"10.7153/jca-2019-15-11","DOIUrl":"https://doi.org/10.7153/jca-2019-15-11","url":null,"abstract":"An upper bound on a linear functional satisfying several constraints is found, then used to provide a short and simple proof of convergence, for orthogonal polynomial expansions. Mathematics subject classification (2010): 42C10, 26D20.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135489","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 a rough ideal convergent of triple sequence spaces de fi ned by Musielak- Orlicz function, using an six dimensional in fi nite matrix, and a generalized geometric difference Zweier six dimensional matrix operator B p ( abc ) of order p . We obtain some topological and algebraic properties of these spaces.
． 利用六维有限矩阵，引入由Musielak- Orlicz函数定义的三序列空间的粗糙理想收敛性，以及p阶的广义几何差分Zweier六维矩阵算子B p (abc)。我们得到了这些空间的一些拓扑和代数性质。
{"title":"On generalized geometric difference of six dimensional rough ideal convergent of triple sequence defined by Musielak-Orlicz function","authors":"A. Esi, N. Subramanian","doi":"10.7153/jca-2019-14-10","DOIUrl":"https://doi.org/10.7153/jca-2019-14-10","url":null,"abstract":". We introduce a rough ideal convergent of triple sequence spaces de fi ned by Musielak- Orlicz function, using an six dimensional in fi nite matrix, and a generalized geometric difference Zweier six dimensional matrix operator B p ( abc ) of order p . We obtain some topological and algebraic properties of these spaces.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134566","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 consider the lower bound of the power exponential function a 2 b + b 2 a for nonnegative real numbers a and b . If a + b = 1, then it is known that the function has the maximum value 1, but it is no known that the minimum value. In this paper, we show that a 2 b + b 2 a > 6083 / 6144 ∼ = 0 . 990072 for nonnegative real numbers a and b with a + b = 1.
{"title":"A lower bound of the power exponential function","authors":"Yusuke Nishizawa","doi":"10.7153/jca-2019-15-01","DOIUrl":"https://doi.org/10.7153/jca-2019-15-01","url":null,"abstract":". In this paper, we consider the lower bound of the power exponential function a 2 b + b 2 a for nonnegative real numbers a and b . If a + b = 1, then it is known that the function has the maximum value 1, but it is no known that the minimum value. In this paper, we show that a 2 b + b 2 a > 6083 / 6144 ∼ = 0 . 990072 for nonnegative real numbers a and b with a + b = 1.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134702","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 present the hyperstability results of a mixed type cubic- quartic func- tional equations in ultrametric Banach spaces.
． 本文给出了一类混合型三次-四次泛函方程在超尺度巴拿赫空间中的超稳定性结果。
{"title":"Hyperstability of a mixed type cubic-quartic functional equation in ultrametric spaces","authors":"Y. Aribou, H. Dimou, S. Kabbaj","doi":"10.7153/jca-2019-14-09","DOIUrl":"https://doi.org/10.7153/jca-2019-14-09","url":null,"abstract":". In this paper, we present the hyperstability results of a mixed type cubic- quartic func- tional equations in ultrametric Banach spaces.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134555","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 recover convergence of a complex sequence (un) out of its summability by weighted means under certain supplementary conditions that control the oscillatory behavior of (un) . As corollaries, we obtain classical Hardy-type Tauberian conditions for various weighted mean methods. Mathematics subject classification (2010): 40A05, 40E05, 40G05.
{"title":"General Tauberian conditions for weighted mean methods of summability","authors":"S. A. Sezer, Ibrahim Çanak","doi":"10.7153/jca-2019-15-08","DOIUrl":"https://doi.org/10.7153/jca-2019-15-08","url":null,"abstract":"In this paper we recover convergence of a complex sequence (un) out of its summability by weighted means under certain supplementary conditions that control the oscillatory behavior of (un) . As corollaries, we obtain classical Hardy-type Tauberian conditions for various weighted mean methods. Mathematics subject classification (2010): 40A05, 40E05, 40G05.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134582","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 the present paper, we consider the Bezier variant of the general family of Gupta-Srivastava operators cite{GS:18}. For the proposed operators, we discuss the rate of convergence by using of Lipschitz type space, Ditzian-Totik modulus of smoothness, weighted modulus of continuity and functions of bounded variation.
{"title":"Rate of convergence of Gupta-Srivastava operators based on certain parameters","authors":"Rameshwar Pratap, N. Deo","doi":"10.7153/jca-2019-14-11","DOIUrl":"https://doi.org/10.7153/jca-2019-14-11","url":null,"abstract":"In the present paper, we consider the Bezier variant of the general family of Gupta-Srivastava operators cite{GS:18}. For the proposed operators, we discuss the rate of convergence by using of Lipschitz type space, Ditzian-Totik modulus of smoothness, weighted modulus of continuity and functions of bounded variation.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44720804","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 the present paper, a general theorem dealing with |A, pn;δ |k summability method of infinite series has been proved by using almost increasing sequences. Some results have also been given. Mathematics subject classification (2010): 26D15, 40D15, 40F05, 40G99.
{"title":"On absolute matrix summability factors of infinite series","authors":"A. Karakas","doi":"10.7153/JCA-2018-13-09","DOIUrl":"https://doi.org/10.7153/JCA-2018-13-09","url":null,"abstract":"In the present paper, a general theorem dealing with |A, pn;δ |k summability method of infinite series has been proved by using almost increasing sequences. Some results have also been given. Mathematics subject classification (2010): 26D15, 40D15, 40F05, 40G99.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":"133-139"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134108","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}
{"title":"On some inequalities concerning relative (p,q)-φ type and relative (p,q)-φ weak type of entire or meromorphic functions with respect to an entire function","authors":"T. Biswas","doi":"10.7153/JCA-2018-13-07","DOIUrl":"https://doi.org/10.7153/JCA-2018-13-07","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":"107-122"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134412","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 discuss Bohr’s inequality for certain classes of analytic functions associated with q -function theory for q ∈ (0,1) . Interestingly, in particular cases when q → 1 , we obtain very fundamental theorems of univalent function theory such as covering and growth theorems for starlike and convex functions. Subsequently, we obtain the Bohr radius for the classes of starlike and convex functions. Mathematics subject classification (2010): 28A25, 30A10, 30B10, 30H05, 39A13.
{"title":"Bohr radius for certain classes of analytic functions","authors":"Sarita Agrawal, M. Mohapatra","doi":"10.7153/JCA-2018-12-10","DOIUrl":"https://doi.org/10.7153/JCA-2018-12-10","url":null,"abstract":"In this paper, we discuss Bohr’s inequality for certain classes of analytic functions associated with q -function theory for q ∈ (0,1) . Interestingly, in particular cases when q → 1 , we obtain very fundamental theorems of univalent function theory such as covering and growth theorems for starlike and convex functions. Subsequently, we obtain the Bohr radius for the classes of starlike and convex functions. Mathematics subject classification (2010): 28A25, 30A10, 30B10, 30H05, 39A13.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":"109-118"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134233","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 and study some basic properties of rough I λ -convergence of weight g , where g : N 3 → [ 0 , ∞ ) is a function satisfying g ( m , n , k ) → ∞ and (cid:3) ( m , n , k ) (cid:3) g ( m , n , k ) (cid:4)→ 0 as m , n , k → ∞ , of triple sequence of Bernstein polynomials and also study the set of all rough I λ -convergence of weight g limits of a triple sequence of Bernstein polynomials and relation between analyticness and rough I λ -convergence of weight g of a triple sequences of Bernstein polynomials.
． 我们引入并研究了权值g的粗糙I λ -收敛的一些基本性质，其中g:N 3→[0,∞)是一个函数满足g (m, N, k)→∞和(cid: 3) (m, N, k) (cid: 3) g (m, N, k) (cid: 4)→0 m, N, k→∞,三重伯恩斯坦多项式序列以及研究的所有粗糙的集合我λ收敛的重量g三重伯恩斯坦多项式序列的极限和关系analyticness我粗略的λ收敛的重量克三伯恩斯坦多项式序列。
{"title":"On triple sequence of Bernstein operator of weighted rough I_λ-convergence","authors":"N. Subramanian, A. Esi","doi":"10.7153/jca-2018-13-02","DOIUrl":"https://doi.org/10.7153/jca-2018-13-02","url":null,"abstract":". We introduce and study some basic properties of rough I λ -convergence of weight g , where g : N 3 → [ 0 , ∞ ) is a function satisfying g ( m , n , k ) → ∞ and (cid:3) ( m , n , k ) (cid:3) g ( m , n , k ) (cid:4)→ 0 as m , n , k → ∞ , of triple sequence of Bernstein polynomials and also study the set of all rough I λ -convergence of weight g limits of a triple sequence of Bernstein polynomials and relation between analyticness and rough I λ -convergence of weight g of a triple sequences of Bernstein polynomials.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":"45-62"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134253","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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