Startseite Mathematik Inequalities for the normalized Jensen functional with applications
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Inequalities for the normalized Jensen functional with applications

  • Hossein Dehghan EMAIL logo
Veröffentlicht/Copyright: 26. April 2016
Veröffentlichen auch Sie bei De Gruyter Brill
Informationen für Autor*innen Erkunden Sie dieses Fachgebiet
Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 1

Abstract

In this paper we present some new inequalities for the normalized Jensen functional which will much improve the famous Jensen’s inequality. We also give some applications in Analysis and Information Theory. Our results refine and generalize the corresponding ones announced in [DRAGOMIR, S. S.: Bounds for the normalised Jensen functional, Bull. Aust. Math. Soc. 74 (2006), 471–478] and [MITANI, K. I. et al.: On sharp triangle inequalities in Banach spaces, J. Math. Anal. Appl. 336 (2007), 1178–1186].

Keywords: plant disease; Jensen’s inequality; convex function; triangle inequality
MSC: Primary 26D15; 26B25

  1. This paper has been communicated by Ján Borsík.

Acknowledgement

The author wishes to thank Professor J. Rooin for proposing Convexity to solve original problem.

References

[1] Aldaz, J. M.: Comparison of differences between arithmetic and geometric means, Tamkang J. Math. 42 (2011), 453–462.10.5556/j.tkjm.42.2011.747Suche in Google Scholar

[2] Dehghan, H.: A characterization of inner product spaces related to the skew-angular distance, Math. Notes 93 (2013), 556–560.10.1134/S0001434613030231Suche in Google Scholar

[3] Dehghan, H.: Some new bounds for the generalized triangle inequality, Math. Inequal. Appl. 12 (2012), 875–881.10.7153/mia-15-75Suche in Google Scholar

[4] Dragomir, S. S.: Bounds for the normalised jensen functional, Bull. Aust. Math. Soc. 74 (2006) 471–478.10.1017/S000497270004051XSuche in Google Scholar

[5] Jian, Z. C.—Ying, C. L.—Cheung, W. S.: On some new Hilbert-type inequalities, Math. Slovaca 61 (2011), 15–28.10.2478/s12175-010-0056-0Suche in Google Scholar

[6] Kato, M.—Saito, K. S.—Tamura, T.: Sharp triangle inequality and its reverse in Banach spaces, Math. Ineqal. Appl. 10 (2007), 451–460.10.7153/mia-10-43Suche in Google Scholar

[7] Mitani, K. I.—Saito, K. S.—Kato, M.—Tamura, T.: On sharp triangle inequalities in Banach spaces, J. Math. Anal. Appl. 336 (2007), 1178–1186.10.1016/j.jmaa.2007.03.036Suche in Google Scholar

[8] Mitrinović, D. S.—Pečarić, J. E.—Fink, A. M.: Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.10.1007/978-94-017-1043-5Suche in Google Scholar

[9] Mitroi, F.-C.: Estimating the normalized Jensen functional, J. Math. Inequal. 5 (2011), 507–521.10.7153/jmi-05-44Suche in Google Scholar

[10] Pečarić J. E.—Prpschan, F.—Tong, Y. L.: Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, MA, 1992.Suche in Google Scholar

Received: 2012-6-20
Accepted: 2013-5-17
Published Online: 2016-4-26
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. Research Article
  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
  8. Lexico groups and direct products of lattice ordered groups
  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
  16. On some modification of Darboux property
  17. Research Article
  18. Separating sets by peripherally continuous functions
  19. Research Article
  20. Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
  21. Research Article
  22. On O’Malley preponderantly continuous functions
  23. Research Article
  24. Inequalities for the normalized Jensen functional with applications
  25. Research Article
  26. Majorization of starlike and convex functions of complex order involving linear operators
  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
  29. Research Article
  30. Central functions for classes of concave univalent functions
  31. Research Article
  32. Inclusion properties for classes of analytic functions associated with conic domains
  33. Research Article
  34. Uniqueness of meromorphic functions and nonlinear differential polynomials sharing a nonzero polynomial
  35. Research Article
  36. Solutions and constrained null-controllability for a differential-difference equation
  37. Research Article
  38. Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale
  39. Research Article
  40. Time periodic solutions for a sixth order nonlinear parabolic equation
  41. Research Article
  42. Some inequalities of trigonometric approximation in weighted Orlicz spaces
  43. Research Article
  44. Summation methods applied to Voronovskaya-type theorems for the partial sums of Fourier series and for Fejér operators
  45. Research Article
  46. Dichotomies for Orlicz spaces
  47. Research Article
  48. On freely generated semigraph C*-algebras
  49. Research Article
  50. Operators with a given part of the numerical range
  51. Research Article
  52. Characterization of quasi-continuity of multifunctions of two variables
  53. Research Paper
  54. Confidence regions in singular weakly nonlinear regression models with constraints
  55. Research Article
  56. Global stability of an SEI model for plant diseases
https://doi.org/10.1515/ms-2015-0121
Schlagwörter für diesen Artikel
plant disease; Jensen’s inequality; convex function; triangle inequality

Artikel in diesem Heft

  1. Research Article
  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
  8. Lexico groups and direct products of lattice ordered groups
  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
  16. On some modification of Darboux property
  17. Research Article
  18. Separating sets by peripherally continuous functions
  19. Research Article
  20. Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
  21. Research Article
  22. On O’Malley preponderantly continuous functions
  23. Research Article
  24. Inequalities for the normalized Jensen functional with applications
  25. Research Article
  26. Majorization of starlike and convex functions of complex order involving linear operators
  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
  29. Research Article
  30. Central functions for classes of concave univalent functions
  31. Research Article
  32. Inclusion properties for classes of analytic functions associated with conic domains
  33. Research Article
  34. Uniqueness of meromorphic functions and nonlinear differential polynomials sharing a nonzero polynomial
  35. Research Article
  36. Solutions and constrained null-controllability for a differential-difference equation
  37. Research Article
  38. Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale
  39. Research Article
  40. Time periodic solutions for a sixth order nonlinear parabolic equation
  41. Research Article
  42. Some inequalities of trigonometric approximation in weighted Orlicz spaces
  43. Research Article
  44. Summation methods applied to Voronovskaya-type theorems for the partial sums of Fourier series and for Fejér operators
  45. Research Article
  46. Dichotomies for Orlicz spaces
  47. Research Article
  48. On freely generated semigraph C*-algebras
  49. Research Article
  50. Operators with a given part of the numerical range
  51. Research Article
  52. Characterization of quasi-continuity of multifunctions of two variables
  53. Research Paper
  54. Confidence regions in singular weakly nonlinear regression models with constraints
  55. Research Article
  56. Global stability of an SEI model for plant diseases
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 15.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2015-0121/pdf
Button zum nach oben scrollen