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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Universal convexity and range problems of shifted hypergeometric functions
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by Toshiyuki Sugawa, Li-Mei Wang and Chengfa Wu;
Proc. Amer. Math. Soc. 152 (2024), 3521-3535
DOI: https://doi.org/10.1090/proc/16849
Published electronically: June 18, 2024

Abstract:

In the present paper, we study the shifted hypergeometric function $f(z)=z_{2}F_{1}(a,b;c;z)$ for real parameters with $0<a\le b\le c$ and its variant $g(z)=z_{2}F_{2}(a,b;c;z^2)$. Our first purpose is to solve the range problems for $f$ and $g$ posed by Ponnusamy and Vuorinen [Rocky Mountain J. Math. 31 (2001), pp. 327–353]. Ruscheweyh, Salinas and Sugawa [Israel J. Math. 171 (2009), pp. 285–304] developed the theory of universal prestarlike functions on the slit domain $\mathbb {C}\setminus [1,+\infty )$ and showed universal starlikeness of $f$ under some assumptions on the parameters. However, there has been no systematic study of universal convexity of the shifted hypergeometric functions except for the case $b=1$. Our second purpose is to show universal convexity of $f$ under certain conditions on the parameters.
References
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Bibliographic Information
  • Toshiyuki Sugawa
  • Affiliation: Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579, Japan
  • MR Author ID: 318760
  • ORCID: 0000-0002-3429-5498
  • Email: sugawa@math.is.tohoku.ac.jp
  • Li-Mei Wang
  • Affiliation: School of Statistics, University of International Business and Economics, No. 10, Huixin Dongjie, Chaoyang District, Beijing 100029, People’s Republic of China
  • Email: wangmabel@163.com
  • Chengfa Wu
  • Affiliation: Institute for Advanced Study, Shenzhen University, Shenzhen 518060, People’s Republic of China; and School of Mathematical Sciences, Shenzhen University, Shenzhen 518060, People’s Republic of China
  • MR Author ID: 1042219
  • ORCID: 0000-0003-1697-4654
  • Email: cfwu@szu.edu.cn
  • Received by editor(s): September 6, 2023
  • Received by editor(s) in revised form: February 14, 2024
  • Published electronically: June 18, 2024
  • Additional Notes: The second author was supported by a grant of University of International Business and Economics (No. 78210418) and National Natural Science Foundation of China (No. 11901086).
    The third author was supported by Shenzhen Natural Science Fund (Stable Support Project of Shenzhen, Grant No. 20231121103530003).
  • Communicated by: Filippo Bracci
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3521-3535
  • MSC (2020): Primary 30C45; Secondary 33C05
  • DOI: https://doi.org/10.1090/proc/16849
  • MathSciNet review: 4767281