대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제34권1호
  • /
  • Pages.239-251
  • /
  • 2019
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON A CLASS OF BIVARIATE MEANS INCLUDING A LOT OF OLD AND NEW MEANS

  • Raissouli, Mustapha (Department of Mathematics Science Faculty Taibah University) ;
  • Rezgui, Anis (Department of Mathematics Science Faculty Taibah University)
  • 투고 : 2018.02.16
  • 심사 : 2018.11.23
  • 발행 : 2019.01.31
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초록

In this paper we introduce a new formulation of symmetric homogeneous bivariate means that depends on the variation of a given continuous strictly increasing function on (0, ${\infty}$). It turns out that this class of means includes a lot of known bivariate means among them the arithmetic mean, the harmonic mean, the geometric mean, the logarithmic mean as well as the first and second Seiffert means. Using this new formulation we introduce a lot of new bivariate means and derive some mean-inequalities.

키워드

TABLE 1.1. Fitted standard means

DBSHCJ_2019_v34n1_239_t0001.png 이미지

참고문헌

  1. B. Q. Feng, The geometric means in Banach *-algebras, J. Operator Theory 57 (2007), no. 2, 243-250.
  2. W. Liao, J. Wu, and J. Zhao, New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant, Taiwanese J. Math. 19 (2015), no. 2, 467-479. https://doi.org/10.11650/tjm.19.2015.4548
  3. M. Raissouli and A. Rezgui, Characterization of homogeneous symmetric monotone bivariate means, J. Inequal. Appl. 2016 (2016), Paper No. 217, 19 pp. https://doi.org/10.1186/s13660-016-0961-z
  4. W. Specht, Zur Theorie der elementaren Mittel, Math. Z 74 (1960), 91-98. https://doi.org/10.1007/BF01180475
  5. M. Tominaga, Specht's ratio in the Young inequality, Sci. Math. Jpn. 55 (2002), no. 3, 583-588.
  6. H. Zuo, G. Shi, and M. Fujii, Refined Young inequality with Kantorovich constant, J. Math. Inequal. 5 (2011), no. 4, 551-556.