DOI QR코드

DOI QR Code

SOME INEQUALITIES FOR THE WEIGHTED CHAOTICALLY GEOMETRIC MEAN

  • Dragomir, Silvestru Sever (Mathematics, College of Engineering & Science, Victoria University)
  • Received : 2019.02.21
  • Accepted : 2019.07.18
  • Published : 2019.08.31

Abstract

In this paper we obtain some new inequalities for the weighted chaotically geometric mean of two positive operators on a complex Hilbert space.

Keywords

operator Inequality;convex functions;arithmetic mean-geometric mean inequality;chaotically geometric mean

References

  1. M. Fujii, J. Micic, J. Pecaric & Y. Seo: Reverse inequalities on chaotically geometric mean via Specht ratio, II. J. Inequal. Pure Appl. Math. 4(2) 2003 Art. 40.
  2. W. Specht: Zer Theorie der elementaren Mittel. Math. Z. 74 (1960), 91-98. https://doi.org/10.1007/BF01180475
  3. S.S. Dragomir: Bounds for the normalized Jensen functional. Bull. Austral. Math. Soc. 74 (2006), no. 3, 417-478.
  4. S.S. Dragomir: A note on Young's inequality. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 111 (2017), no. 2, 349-354. Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 126. [Onlinehttp://rgmia.org/papers/v18/v18a126.pdf]. https://doi.org/10.1007/s13398-016-0300-8
  5. M. Tominaga: Specht's ratio in the Young inequality. Sci. Math. Japon. 55 (2002), 583-588.
  6. S.S. Dragomir: A note on new refinements and reverses of Young's inequality. Transylv. J. Math. Mech. 8 (2016), no. 1, 45-49. Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 131. [Online http://rgmia.org/papers/v18/v18a131.pdf].
  7. M. Fujii, S.H. Lee, Y. Seo & D. Jung: Reverse inequalities on chaotically geometric mean via Specht ratio. Math. Inequal. Appl. 6 (2003), no. 3, 509-519.