Jensen and Ostrowski type inequalities for general Lebesgue integral with applications

Sever Dragomir

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2016)

  • Volume: 70, Issue: 2
  • ISSN: 0365-1029

Abstract

top
Some inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for f-divergence measure are provided as well.

How to cite

top

Sever Dragomir. "Jensen and Ostrowski type inequalities for general Lebesgue integral with applications." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 70.2 (2016): null. <http://eudml.org/doc/289755>.

@article{SeverDragomir2016,
abstract = {Some inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for f-divergence measure are provided as well.},
author = {Sever Dragomir},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Ostrowski’s inequality; Jensen’s inequality; f-divergence measures},
language = {eng},
number = {2},
pages = {null},
title = {Jensen and Ostrowski type inequalities for general Lebesgue integral with applications},
url = {http://eudml.org/doc/289755},
volume = {70},
year = {2016},
}

TY - JOUR
AU - Sever Dragomir
TI - Jensen and Ostrowski type inequalities for general Lebesgue integral with applications
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2016
VL - 70
IS - 2
SP - null
AB - Some inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for f-divergence measure are provided as well.
LA - eng
KW - Ostrowski’s inequality; Jensen’s inequality; f-divergence measures
UR - http://eudml.org/doc/289755
ER -

References

top
  1. Bhattacharyya, A., On a measure of divergence between two statistical populations defined by their probability distributions, Bull. Calcutta Math. Soc. 35 (1943), 99-109. 
  2. Cerone, P., Dragomir, S. S., Midpoint-type rules from an inequalities point of view, in Handbook of Analytic-Computational Methods in Applied Mathematics, Anastassiou, G. A., (Ed.), CRC Press, New York, 2000, 135-200. 
  3. Cerone, P., Dragomir, S. S., Roumeliotis, J., Some Ostrowski type inequalities for n-time differentiable mappings and applications, Demonstratio Math. 32 (2) (1999), 697-712. 
  4. Csiszar, I. I., Information-type measures of difference of probability distributions and indirect observations, Studia Math. Hungarica 2 (1967), 299-318. 
  5. Dragomir, S. S., Ostrowski’s inequality for monotonous mappings and applications, J. KSIAM 3 (1) (1999), 127-135. 
  6. Dragomir, S. S., The Ostrowski’s integral inequality for Lipschitzian mappings and applications, Comp. Math. Appl. 38 (1999), 33-37. 
  7. Dragomir, S. S., The Ostrowski integral inequality for mappings of bounded variation, Bull. Austral. Math. Soc. 60 (1) (1999), 495-508. 
  8. Dragomir, S. S., A converse result for Jensen’s discrete inequality via Gruss’ inequality and applications in information theory, An. Univ. Oradea Fasc. Mat. 7 (1999/2000), 178-189. 
  9. Dragomir, S. S., On the Ostrowski’s integral inequality for mappings with bounded variation and applications, Math. Inequal. Appl. 4 (1) (2001), 59-66. 
  10. Dragomir, S. S., On a reverse of Jessen’s inequality for isotonic linear functionals, J. Ineq. Pure Appl. Math. 2, No. 3, (2001), Art. 36. 
  11. Dragomir, S. S., An Ostrowski like inequality for convex functions and applications, Revista Math. Complutense 16 (2) (2003), 373-382. 
  12. Dragomir, S. S., Reverses of the Jensen inequality in terms of the first derivative and applications, Acta Math. Vietnam. 38, no. 3 (2013), 429-446. Preprint RGMIA Res. Rep. Coll. 14 (2011), Art. 71. [Online http://rgmia.org/papers/v14/v14a71.pdf]. 
  13. Dragomir, S. S., Operator Inequalities of Ostrowski and Trapezoidal Type, Springer, New York, 2012. 
  14. Dragomir, S. S., Perturbed companions of Ostrowski’s inequality for absolutely continuous functions (I), An. Univ. Vest Timi¸s. Ser. Mat.-Inform. 54, no. 1 (2016), 119-138. Preprint RGMIA Res. Rep. Coll. 17 (2014), Art 7, 15 pp. [Online http://rgmia.org/papers/v17/v17a07.pdf]. 
  15. Dragomir, S. S., General Lebesgue integral inequalities of Jensen and Ostrowski type for differentiable functions whose derivatives in absolute value are h-convex and applications, Ann. Univ. Mariae Curie-Skłodowska Sect. A 69, no. 2 (2015), 17-45. 
  16. Dragomir, S. S., Cerone, P., Roumeliotis, J., Wang, S., A weighted version of Ostrowski inequality for mappings of H¨older type and applications in numerical analysis, Bull. Math. Soc. Sci. Math. Romanie 42(90) (4) (1999), 301-314. 
  17. Dragomir, S. S., Ionescu, N. M., Some converse of Jensen’s inequality and applications, Rev. Anal. Num´er. Th´eor. Approx. 23, No. 1 (1994), 71-78. 
  18. Dragomir, S. S., Rassias, Th. M. (Eds.), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publishers, Dordrecht-Boston-London, 2002. 
  19. Hellinger, E., Neue Bergr¨uirdung du Theorie quadratisher Formerus von 
  20. uneudlichvieleu Ver¨anderlicher, J. Reine Angew. Math. 36 (1909), 210-271. 
  21. Jeffreys, H., An invariant form for the prior probability in estimating problems, Proc. Roy. Soc. London A Math. Phys. Sci. 186 (1946), 453461. 
  22. Kapur, J. N., A comparative assessment of various measures of directed divergence, Advances in Management Studies 3 (1984), 1-16. 
  23. Kullback, S., Leibler, R. A., On information and sufficiency, Annals Math. Statist. 22 (1951), 79-86. 
  24. Ostrowski, A., Uber die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert, Comment. Math. Helv. 10 (1938), 226-227. 
  25. Taneja, I. J., Generalised Information Measures and Their Applications [Online http://www.mtm.ufsc.br/~taneja/bhtml/bhtml.html]. 
  26. Topsoe, F., Some inequalities for information divergence and related measures of discrimination, Preprint RGMIA Res. Rep. Coll. 2 (1) (1999), 85-98. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.