{"title":"Extremal Problems of Turán-type Involving the Location of All Zeros of a Class of Rational Functions","authors":"M. Y. Mir, S. L. Wali, W. M. Shah","doi":"10.1134/s1063454124700122","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we prove a Turán-type inequality for rational functions and thereby extend it to a more general class of rational functions <span>\\(r(s(z))\\)</span> of degree <i>mn</i> with prescribed poles, where <span>\\(s(z)\\)</span> is a polynomial of degree <i>m</i>. These results not only generalize some Turán-type inequalities for rational functions, but also improve as well as generalize some known polynomial inequalities.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"43 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik St Petersburg University-Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1063454124700122","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we prove a Turán-type inequality for rational functions and thereby extend it to a more general class of rational functions \(r(s(z))\) of degree mn with prescribed poles, where \(s(z)\) is a polynomial of degree m. These results not only generalize some Turán-type inequalities for rational functions, but also improve as well as generalize some known polynomial inequalities.
期刊介绍：
Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.
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