대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권1호
  • /
  • Pages.153-161
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  • 2023
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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DETECTABLE MEANS AND APPLICATIONS

  • Mustapha Raissouli (Department of Mathematics Science Faculty Moulay Ismail University)
  • 투고 : 2022.02.10
  • 심사 : 2022.05.25
  • 발행 : 2023.01.31
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초록

In this paper, we introduce a new concept for bivariate means and we study its properties. Application of this concept for mean-inequalities is also discussed. Open problems are derived as well.

키워드

과제정보

The author would like to thank the anonymous referee for his/her valuable comments and suggestions which have been included in the final version of this manuscript.

참고문헌

  1. M. C. Anisiu and V. Anisiu, The first Seiffert mean is strictly (G, A)-super-stabilizable, J. Inequal. Appl. 2014 (2014), 185, 7 pp. https://doi.org/10.1186/1029-242X-2014-185
  2. P. S. Bullen, Handbook of Means and Their Inequalities, Mathematics and its Applications, 560, Kluwer Academic Publishers Group, Dordrecht, 2003. https://doi.org/10.1007/978-94-017-0399-4
  3. Y.-M. Chu and B.-Y. Long, Bounds of the Neuman-Sandor mean using power and identric means, Abstr. Appl. Anal. 2013 (2013), Art. ID 832591, 6 pp. https://doi.org/10.1155/2013/832591
  4. Y.-M. Chu, B.-Y. Long, W. Gong, and Y. Song, Sharp bounds for Seiffert and Neuman-Sandor means in terms of generalized logarithmic means, J. Inequal. Appl. 2013 (2013), 10, 13 pp. https://doi.org/10.1186/1029-242X-2013-10
  5. F. Hiai and H. Kosaki, Means for matrices and comparison of their norms, Indiana Univ. Math. J. 48 (1999), no. 3, 899-936. https://doi.org/10.1512/iumj.1999.48.1665
  6. W.-D. Jiang and F. Qi, Sharp bounds for Neuman-Sandor's mean in terms of the root-mean-square, Period. Math. Hungar. 69 (2014), no. 2, 134-138. https://doi.org/10.1007/s10998-014-0057-9
  7. W.-D. Jiang and F. Qi, Sharp bounds for the Neuman-Sandor mean in terms of the power and contraharmonic means, Cogent Math. 2 (2015), Art. ID 995951, 7 pp. https://doi.org/10.1080/23311835.2014.995951
  8. E. Neuman and J. Sandor, On the Schwab-Borchardt mean, Math. Pannon. 14 (2003), no. 14, 253-266.
  9. E. Neuman and J. Sandor, On the Schwab-Borchardt mean. II, Math. Pannon. 17 (2006), no. 1, 49-59.
  10. M. Raissouli, Stability and stabilizability for means, Appl. Math. E-Notes 11 (2011), 159-174.
  11. M. Raissouli, Stabilizability of the Stolarsky mean and its approximation in terms of the power binomial mean, Int. J. Math. Anal. (Ruse) 6 (2012), no. 17-20, 871-881.
  12. M. Raissouli, Refinements for mean-inequalities via the stabilizability concept, J. Ineq. Appl. 2012 (2012), 26 pages.
  13. M. Raissouli and J. Sandor, On a method of construction of new means with applications, J. Inequal. Appl. 2013 (2013), 89, 18 pp. https://doi.org/10.1186/1029-242X-2013-89
  14. M. Raissouli and J. Sandor, Sub-stabilizable and super-stabilizable bivariate means, J. Ineq. Appl. 2014 (2014), Art. 28.
  15. M. Raissouli and J. Sandor, Sub-super-stabilizability of certain bivariate means via mean-convexity, J. Inequal. Appl. 2016 (2016), Paper No. 273, 13 pp. https://doi.org/10.1186/s13660-016-1212-z
  16. J. Sandor, Monotonicity and convexity properties of means, Octogon Math. Mag. 7 (1999), no. 2, 22-27.
  17. H. J. Seiffert, Problem 887, Nieuw Arch. Wisk. 11 (1993), 176.
  18. H. J. Seiffert, Aufgabe 16, Wurzel 29 (1995), 87.