Jensen and Ostrowski type inequalities for general Lebesgue integral with applications

Sever Dragomir

Abstract


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

Keywords


Ostrowski’s inequality; Jensen’s inequality; f-divergence measures

Full Text:

PDF

References


Bhattacharyya, A., On a measure of divergence between two statistical populations defined by their probability distributions, Bull. Calcutta Math. Soc. 35 (1943), 99-109.

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.

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.

Csiszar, I. I., Information-type measures of difference of probability distributions and indirect observations, Studia Math. Hungarica 2 (1967), 299-318.

Dragomir, S. S., Ostrowski’s inequality for monotonous mappings and applications, J. KSIAM 3 (1) (1999), 127-135.

Dragomir, S. S., The Ostrowski’s integral inequality for Lipschitzian mappings and applications, Comp. Math. Appl. 38 (1999), 33-37.

Dragomir, S. S., The Ostrowski integral inequality for mappings of bounded variation, Bull. Austral. Math. Soc. 60 (1) (1999), 495-508.

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.

Dragomir, S. S., On the Ostrowski’s integral inequality for mappings with bounded variation and applications, Math. Inequal. Appl. 4 (1) (2001), 59-66.

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.

Dragomir, S. S., An Ostrowski like inequality for convex functions and applications, Revista Math. Complutense 16 (2) (2003), 373-382.

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].

Dragomir, S. S., Operator Inequalities of Ostrowski and Trapezoidal Type, Springer, New York, 2012.

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].

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.

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.

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.

Dragomir, S. S., Rassias, Th. M. (Eds.), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publishers, Dordrecht-Boston-London, 2002.

Hellinger, E., Neue Bergr¨uirdung du Theorie quadratisher Formerus von

uneudlichvieleu Ver¨anderlicher, J. Reine Angew. Math. 36 (1909), 210-271.

Jeffreys, H., An invariant form for the prior probability in estimating problems, Proc. Roy. Soc. London A Math. Phys. Sci. 186 (1946), 453461.

Kapur, J. N., A comparative assessment of various measures of directed divergence, Advances in Management Studies 3 (1984), 1-16.

Kullback, S., Leibler, R. A., On information and sufficiency, Annals Math. Statist. 22 (1951), 79-86.

Ostrowski, A., Uber die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert, Comment. Math. Helv. 10 (1938), 226-227.

Taneja, I. J., Generalised Information Measures and Their Applications [Online http://www.mtm.ufsc.br/~taneja/bhtml/bhtml.html].

Topsoe, F., Some inequalities for information divergence and related measures of discrimination, Preprint RGMIA Res. Rep. Coll. 2 (1) (1999), 85-98.




DOI: http://dx.doi.org/10.17951/a.2016.70.2.29
Date of publication: 2016-12-24 22:42:01
Date of submission: 2016-12-23 20:27:36


Statistics


Total abstract view - 800
Downloads (from 2020-06-17) - PDF - 465

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 Sever Dragomir