{"title":"Uniqueness Result Concerning First Derivative and Difference of a Meromorphic Function andSufficient Condition for Periodicity","authors":"S. Majumder, N. Sarkar","doi":"10.3103/s1068362324700109","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In the paper, we discuss the uniqueness problem of meromorphic function <span>\\(f(z)\\)</span> when <span>\\(f^{\\prime}(z)\\)</span> shares <span>\\(a\\)</span>, <span>\\(b\\)</span> and <span>\\(\\infty\\)</span> CM with <span>\\(\\Delta_{c}f(z)\\)</span>, where <span>\\(a\\)</span> and <span>\\(b\\)</span> are two distinct finite values. The obtained result improves the recent result of Qi et al. [6] by dropping the condition ‘‘order of growth of <span>\\(f\\)</span> is not an integer or infinite’’ by ‘‘<span>\\(\\rho(f)<\\infty\\)</span>’’. Also in the paper we give an affirmative answer of the question raised by Wei et al. [9].</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"16 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3103/s1068362324700109","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In the paper, we discuss the uniqueness problem of meromorphic function \(f(z)\) when \(f^{\prime}(z)\) shares \(a\), \(b\) and \(\infty\) CM with \(\Delta_{c}f(z)\), where \(a\) and \(b\) are two distinct finite values. The obtained result improves the recent result of Qi et al. [6] by dropping the condition ‘‘order of growth of \(f\) is not an integer or infinite’’ by ‘‘\(\rho(f)<\infty\)’’. Also in the paper we give an affirmative answer of the question raised by Wei et al. [9].
期刊介绍：
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) is an outlet for research stemming from the widely acclaimed Armenian school of theory of functions, this journal today continues the traditions of that school in the area of general analysis. A very prolific group of mathematicians in Yerevan contribute to this leading mathematics journal in the following fields: real and complex analysis; approximations; boundary value problems; integral and stochastic geometry; differential equations; probability; integral equations; algebra.
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