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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The function $(b^x-a^x)/x$: Inequalities and properties
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by Feng Qi and Sen-Lin Xu PDF
Proc. Amer. Math. Soc. 126 (1998), 3355-3359 Request permission

Abstract:

In the article, some properties and inequalities of the function $\int _{a}^{b}t^{x-1}\text {d}t$ are given by analytic method and the mathematical induction.
References
  • Ji Chang Kuang, Changyong budengshi, 2nd ed., Hunan Jiaoyu Chubanshe, Changsha, 1993 (Chinese, with English summary). With a preface by Shan Zhen Lu. MR 1305610
  • Feng Qi, Refinements and Extensions of an Inequality, Mathematics and Informatics Quarterly (to appear).
  • Feng Qi, On a Two-parameter Family of Nonhomogeneous Mean Values, Tamkang Journal of Mathematics, Vol. 29 (1998), no. 2.
  • D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Classical and new inequalities in analysis, Mathematics and its Applications (East European Series), vol. 61, Kluwer Academic Publishers Group, Dordrecht, 1993. MR 1220224, DOI 10.1007/978-94-017-1043-5
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Additional Information
  • Feng Qi
  • Affiliation: Department of Mathematics, Jiaozuo Institute of Technology, Jiaozuo City, Henan 454000, People’s Republic of China
  • MR Author ID: 610520
  • ORCID: 0000-0001-6239-2968
  • Email: qifeng@math.ustc.edu.cn, qifeng@jzit.edu.cn
  • Sen-Lin Xu
  • Affiliation: Department of Mathematics, Jiaozuo Institute of Technology, Jiaozuo City, Henan 454000, People’s Republic of China; Department of Mathematics, University of Sciences and Technology of China, Hefei City, Anhui 230026, People’s Republic of China
  • Received by editor(s): July 17, 1996
  • Received by editor(s) in revised form: April 8, 1997
  • Additional Notes: The first author was partially supported by NSF grant 974050400 of Henan Province, People’s Republic of China.
  • Communicated by: J. Marshall Ash
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 3355-3359
  • MSC (1991): Primary 26A48; Secondary 26D07
  • DOI: https://doi.org/10.1090/S0002-9939-98-04442-6
  • MathSciNet review: 1459146