{"title":"On some geometric results for generalized k-Bessel functions","authors":"Evrim Toklu","doi":"10.1515/dema-2022-0235","DOIUrl":null,"url":null,"abstract":"Abstract The main aim of this article is to present some novel geometric properties for three distinct normalizations of the generalized k k -Bessel functions, such as the radii of uniform convexity and of α \\alpha -convexity. In addition, we show that the radii of α \\alpha -convexity remain in between the radii of starlikeness and convexity, in the case when α ∈ [ 0 , 1 ] , \\alpha \\in {[}0,1], and they are decreasing with respect to the parameter α . \\alpha . The key tools in the proof of our main results are infinite product representations for normalized k k -Bessel functions and some properties of real zeros of these functions.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"56 1","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Demonstratio Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/dema-2022-0235","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract The main aim of this article is to present some novel geometric properties for three distinct normalizations of the generalized k k -Bessel functions, such as the radii of uniform convexity and of α \alpha -convexity. In addition, we show that the radii of α \alpha -convexity remain in between the radii of starlikeness and convexity, in the case when α ∈ [ 0 , 1 ] , \alpha \in {[}0,1], and they are decreasing with respect to the parameter α . \alpha . The key tools in the proof of our main results are infinite product representations for normalized k k -Bessel functions and some properties of real zeros of these functions.
期刊介绍：
Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.
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