Pub Date : 2021-11-01DOI: 10.15393/j3.art.2021.10911
E. Mazepa, D. K. Ryaboshlykova
{"title":"Boundary-value problems for the inhomogeneous Schr\"odinger equation with variations of its potential on non-compact Riemannian manifolds","authors":"E. Mazepa, D. K. Ryaboshlykova","doi":"10.15393/j3.art.2021.10911","DOIUrl":"https://doi.org/10.15393/j3.art.2021.10911","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"87 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83807505","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}
Pub Date : 2021-11-01DOI: 10.15393/j3.art.2021.10910
K. P. Isaev, R. S. Yulmukhametov
{"title":"Equivalent conditions for the existence of unconditional bases of reproducing kernels in spaces of entire functions","authors":"K. P. Isaev, R. S. Yulmukhametov","doi":"10.15393/j3.art.2021.10910","DOIUrl":"https://doi.org/10.15393/j3.art.2021.10910","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"37 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81454409","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}
Pub Date : 2021-11-01DOI: 10.15393/j3.art.2021.10270
V. Danchenko, D. Chkalova
{"title":"Bernstein-Type Estimates for the Derivatives of Trigonometric Polynomials","authors":"V. Danchenko, D. Chkalova","doi":"10.15393/j3.art.2021.10270","DOIUrl":"https://doi.org/10.15393/j3.art.2021.10270","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"42 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82220932","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}
Pub Date : 2020-11-01DOI: 10.15393/j3.art.2020.8830
S. Dragomir
. Let f be an convex function on the convex set C in a linear space and x; y 2 C; with x 6 = y: If p : [0 ; 1] ! [0 ; 1 ) is Lebesgue integrable and symmetric, namely p (1 t = p ( t for all 2 [0 ; 1] ; then where r (cid:6) f ( ) are the G(cid:226)teaux lateral derivatives. Some applications for norms and semi-inner products are also provided.
． 设f是线性空间中凸集C和x上的一个凸函数;y 2 C;如果p = [0];1) ![0;1)是Lebesgue可积对称的，即p (1) t = p (t对于所有2 [0];1);式中r (cid:6) f()为G(cid:226)对侧导数。给出了规范和半内产品的一些应用。
{"title":"REFINEMENTS AND REVERSES OF F ́EJER’S INEQUALITIES FOR CONVEX FUNCTIONS ON LINEAR SPACES","authors":"S. Dragomir","doi":"10.15393/j3.art.2020.8830","DOIUrl":"https://doi.org/10.15393/j3.art.2020.8830","url":null,"abstract":". Let f be an convex function on the convex set C in a linear space and x; y 2 C; with x 6 = y: If p : [0 ; 1] ! [0 ; 1 ) is Lebesgue integrable and symmetric, namely p (1 t = p ( t for all 2 [0 ; 1] ; then where r (cid:6) f ( ) are the G(cid:226)teaux lateral derivatives. Some applications for norms and semi-inner products are also provided.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"17 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79245467","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}
Pub Date : 2020-08-03DOI: 10.15393/j3.art.2022.11550
Yu-Lin Chou
We show that, on any given finite Borel measure space with the ambient space being a Polish metric space, every Borel real-valued function is almost a bounded, uniformly continuous function in the sense that for every $varepsilon > 0$ there is some bounded, uniformly continuous function such that the set of points at which they would not agree has measure $< varepsilon$. In particular, this result complements the known result of almost uniform continuity of Borel real-valued functions on a finite Radon measure space whose ambient space is a locally compact metric space. As direct applications in connection with some common modes of convergence, under our assumptions it holds that i) for every Borel real-valued function there is some sequence of bounded, uniformly continuous functions converging in measure to it, and ii) for every bounded, Borel real-valued function there is some sequence of bounded, uniformly continuous functions converging in $L^{p}$ to it.
{"title":"A Note on Almost Uniform Continuity of Borel Functions on Polish Metric Spaces","authors":"Yu-Lin Chou","doi":"10.15393/j3.art.2022.11550","DOIUrl":"https://doi.org/10.15393/j3.art.2022.11550","url":null,"abstract":"We show that, on any given finite Borel measure space with the ambient space being a Polish metric space, every Borel real-valued function is almost a bounded, uniformly continuous function in the sense that for every $varepsilon > 0$ there is some bounded, uniformly continuous function such that the set of points at which they would not agree has measure $< varepsilon$. In particular, this result complements the known result of almost uniform continuity of Borel real-valued functions on a finite Radon measure space whose ambient space is a locally compact metric space. As direct applications in connection with some common modes of convergence, under our assumptions it holds that i) for every Borel real-valued function there is some sequence of bounded, uniformly continuous functions converging in measure to it, and ii) for every bounded, Borel real-valued function there is some sequence of bounded, uniformly continuous functions converging in $L^{p}$ to it.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"30 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73331254","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}
Pub Date : 2020-06-01DOI: 10.15393/j3.art.2020.6750
S. Mohammed, Azam Akbar
{"title":"Fixed Point Theorems of Fuzzy Set-Valued Maps with Applications","authors":"S. Mohammed, Azam Akbar","doi":"10.15393/j3.art.2020.6750","DOIUrl":"https://doi.org/10.15393/j3.art.2020.6750","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"55 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90126838","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}
Pub Date : 2020-06-01DOI: 10.15393/j3.art.2020.6950
V. S. Kumar, R. B. Sharma
{"title":"ZALCMAN CONJECTURE AND HANKEL DETERMINANT OF ORDER THREE FOR STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH SHELL-LIKE CURVES","authors":"V. S. Kumar, R. B. Sharma","doi":"10.15393/j3.art.2020.6950","DOIUrl":"https://doi.org/10.15393/j3.art.2020.6950","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"12 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85456039","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}
Pub Date : 2020-06-01DOI: 10.15393/j3.art.2020.7930
F. Garif’yanov, E. Strezhneva
{"title":"THE SUMMARY EQUATION FOR FUNCTIONS ANALYTICAL OUTSIDE FOUR SQUARES. APPLICATIONS","authors":"F. Garif’yanov, E. Strezhneva","doi":"10.15393/j3.art.2020.7930","DOIUrl":"https://doi.org/10.15393/j3.art.2020.7930","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"260 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76768999","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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