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Convergence of General Fourier Series of Differentiable Functions 可微分函数的一般傅里叶级数的收敛性
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-12-28 DOI: 10.3103/s1068362323060067
V. Tsagareishvili
{"title":"Convergence of General Fourier Series of Differentiable Functions","authors":"V. Tsagareishvili","doi":"10.3103/s1068362323060067","DOIUrl":"https://doi.org/10.3103/s1068362323060067","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Convergence of classical Fourier series (trigonometric, Haar, Walsh, <span>(dots)</span> systems) of differentiable functions are trivial problems and they are well known. But general Fourier series, as it is known, even for the function <span>(f(x)=1)</span> does not converge. In such a case, if we want differentiable functions with respect to the general orthonormal system (ONS) <span>((varphi_{n}))</span> to have convergent Fourier series, we must find the special conditions on the functions <span>(varphi_{n})</span> of system <span>((varphi_{n}))</span>. This problem is studied in the present paper. It is established that the resulting conditions are best possible. Subsystems of general orthonormal systems are considered.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066579","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}
引用次数: 0
Orientation-Dependent Chord Length Distribution in a Convex Quadrilateral 凸四边形中与方向有关的弦长分布
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-12-28 DOI: 10.3103/s1068362323060055
D. M. Martirosyan
{"title":"Orientation-Dependent Chord Length Distribution in a Convex Quadrilateral","authors":"D. M. Martirosyan","doi":"10.3103/s1068362323060055","DOIUrl":"https://doi.org/10.3103/s1068362323060055","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This work contributes to the research devoted to the recognition of a convex body by probabilistic characteristics of its lower-dimensional sections. In this paper, for any convex quadrilateral, five orientation-dependent characteristics are introduced and explicitly evaluated per direction. In terms of these characteristics, simple explicit representations of the orientation-dependent chord length distribution function and the covariogram are obtained not only for an arbitrary convex quadrilateral but also for any right prism based on it.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066578","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}
引用次数: 0
Derivatives of Meromorphic Functions Sharing Polynomials with Their Difference Operators 与它们的差分算子共享多项式的单项式函数的衍生物
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-12-28 DOI: 10.3103/s1068362323060079
M.-H. Wang, J.-F. Chen
{"title":"Derivatives of Meromorphic Functions Sharing Polynomials with Their Difference Operators","authors":"M.-H. Wang, J.-F. Chen","doi":"10.3103/s1068362323060079","DOIUrl":"https://doi.org/10.3103/s1068362323060079","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we investigate the uniqueness of meromorphic functions of finite order <span>(f(z))</span> concerning their difference operators <span>(Delta_{c}f(z))</span> and derivatives <span>(f^{prime}(z))</span> and prove that if <span>(Delta_{c}f(z))</span> and <span>(f^{prime}(z))</span> share <span>(a(z))</span>, <span>(b(z))</span>, <span>(infty)</span> CM, where <span>(a(z))</span> and <span>(b(z))</span> are two distinct polynomials, then they assume one of following cases: <span>((1))</span>\u0000<span>(f^{prime}(z)equivDelta_{c}f(z))</span>; <span>((2))</span>\u0000<span>(f(z))</span> reduces to a polynomial and <span>(f^{prime}(z)-ADelta_{c}f(z)equiv(1-A)(c_{n}z^{n}+c_{n-1}z^{n-1}+cdots+c_{1}z+c_{0}))</span>, where <span>(A(neq 1))</span> is a nonzero constant and <span>(c_{n},c_{n-1},cdots,c_{1},c_{0})</span> are all constants. This generalizes the corresponding results due to Qi et al. and Deng et al.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066586","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}
引用次数: 0
Erratum to: Some Results on Nonlinear Difference-Differential Equations 关于非线性微分-微分方程的一些结果的勘误
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-19 DOI: 10.3103/s1068362323300015
L. L. Wu, M. L. Liu#, P. C. Hu
{"title":"Erratum to: Some Results on Nonlinear Difference-Differential Equations","authors":"L. L. Wu, M. L. Liu#, P. C. Hu","doi":"10.3103/s1068362323300015","DOIUrl":"https://doi.org/10.3103/s1068362323300015","url":null,"abstract":"<p>An Erratum to this paper has been published: https://doi.org/10.3103/S1068362323300015</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138509344","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}
引用次数: 0
Comparison of Polynomials and Weighted-Hyperbolic Operators 多项式与加权双曲算子的比较
4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-01 DOI: 10.3103/s1068362323050023
M. A. Khachaturyan, V. N. Margaryan
{"title":"Comparison of Polynomials and Weighted-Hyperbolic Operators","authors":"M. A. Khachaturyan, V. N. Margaryan","doi":"10.3103/s1068362323050023","DOIUrl":"https://doi.org/10.3103/s1068362323050023","url":null,"abstract":"","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135963494","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}
引用次数: 0
A Hardy–Littlewood Type Theorem for Harmonic Bergman–Orlicz Spaces and Applications 调和Bergman-Orlicz空间的Hardy-Littlewood型定理及其应用
4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-01 DOI: 10.3103/s1068362323050096
Xi Fu, Q. Shi#
{"title":"A Hardy–Littlewood Type Theorem for Harmonic Bergman–Orlicz Spaces and Applications","authors":"Xi Fu, Q. Shi#","doi":"10.3103/s1068362323050096","DOIUrl":"https://doi.org/10.3103/s1068362323050096","url":null,"abstract":"","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135963668","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}
引用次数: 0
Operator Preserving Bernstein-Type Inequalities between Polynomials 多项式间保算子bernstein型不等式
4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-01 DOI: 10.3103/s1068362323050059
A. Mir, A. Hussain
{"title":"Operator Preserving Bernstein-Type Inequalities between Polynomials","authors":"A. Mir, A. Hussain","doi":"10.3103/s1068362323050059","DOIUrl":"https://doi.org/10.3103/s1068362323050059","url":null,"abstract":"","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135963505","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}
引用次数: 0
On a Generalization of an Operator Preserving Turán-Type Inequality for Complex Polynomials 复多项式算子保持Turán-Type不等式的推广
4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-01 DOI: 10.3103/s1068362323050047
S. A. Malik, B. A. Zargar
{"title":"On a Generalization of an Operator Preserving Turán-Type Inequality for Complex Polynomials","authors":"S. A. Malik, B. A. Zargar","doi":"10.3103/s1068362323050047","DOIUrl":"https://doi.org/10.3103/s1068362323050047","url":null,"abstract":"Abstract Let $$W(zeta)=(a_{0}+a_{1}zeta+...+a_{n}zeta^{n})$$ be a polynomial of degree $$n$$ having all its zeros in $$mathbb{T}_{k}cupmathbb{E}^{-}_{k}$$ , $$kgeq 1$$ , then for every real or complex number $$alpha$$ with $$|alpha|geq 1+k+k^{n}$$ , Govil and McTume [7] showed that the following inequality holds $$maxlimits_{zetainmathbb{T}_{1}}|D_{alpha}W(zeta)|geq nleft(frac{|alpha|-k}{1+k^{n}}right)||W||+nleft(frac{|alpha|-(1+k+k^{n})}{1+k^{n}}right)minlimits_{zetainmathbb{T}_{k}}|W(zeta)|.$$ In this paper, we have obtained a generalization of this inequality involving sequence of operators known as polar derivatives. In addition, the problem for the limiting case is also considered.","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135963522","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}
引用次数: 0
Distribution of Zeros and Critical Points of a Polynomial, and Sendov’s Conjecture 多项式零点和临界点的分布及Sendov猜想
4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-01 DOI: 10.3103/s1068362323050084
G. M. Sofi, W. M. Shah
{"title":"Distribution of Zeros and Critical Points of a Polynomial, and Sendov’s Conjecture","authors":"G. M. Sofi, W. M. Shah","doi":"10.3103/s1068362323050084","DOIUrl":"https://doi.org/10.3103/s1068362323050084","url":null,"abstract":"Abstract According to the Gauss–Lucas theorem, the critical points of a complex polynomial $$p(z):=sum_{j=0}^{n}a_{j}z^{j}$$ where $$a_{j}inmathbb{C}$$ always lie in the convex hull of its zeros. In this paper, we prove certain relations between the distribution of zeros of a polynomial and its critical points. Using these relations, we prove the well-known Sendov’s conjecture for certain special cases.","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135963691","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}
引用次数: 0
Effectiveness of the Even-Type Delayed Mean in Approximation of Conjugate Functions 偶型延迟均值在共轭函数逼近中的有效性
4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-01 DOI: 10.3103/s1068362323050035
Xh. Z. Krasniqi
{"title":"Effectiveness of the Even-Type Delayed Mean in Approximation of Conjugate Functions","authors":"Xh. Z. Krasniqi","doi":"10.3103/s1068362323050035","DOIUrl":"https://doi.org/10.3103/s1068362323050035","url":null,"abstract":"","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135964017","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}
引用次数: 0
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