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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The function ${\mathbf{(}b^{x}-a^{x})/x:}$ inequalities and properties


Authors: Feng Qi and Sen-Lin Xu
Journal: Proc. Amer. Math. Soc. 126 (1998), 3355-3359
MSC (1991): Primary 26A48; Secondary 26D07
MathSciNet review: 1459146
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. 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 (95j:26001)
  • 2. Feng Qi, Refinements and Extensions of an Inequality, Mathematics and Informatics Quarterly (to appear).
  • 3. Feng Qi, On a Two-parameter Family of Nonhomogeneous Mean Values, Tamkang Journal of Mathematics, Vol. 29 (1998), no. 2.
  • 4. 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 (94c:00004)

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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
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

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04442-6
PII: S 0002-9939(98)04442-6
Keywords: Absolutely monotonic, completely monotonic, absolutely convex, regularly monotonic, property, inequality, mathematical induction, Tchebycheff integral inequality
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
Article copyright: © Copyright 1998 American Mathematical Society