On the refinements of Jensen Mercer's inequality

Authors

  • M. Adil Khan University of Peshawar, India
  • Asif R. Khan University of Karachi, Pakistan
  • J. Pečarić University of Zagreb, Croatia

DOI:

https://doi.org/10.33993/jnaat411-969

Keywords:

convex functions, Jensen's Mercer's inequality, \(n\)-exponential convexity
Abstract views: 342

Abstract

In this paper we give refinements of Jensen-Mercer's inequality and its generalizations and give applications for means. We prove \(n\)-exponential convexity of the functions constructed from these refinements. At the end we discuss some examples.

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References

M. Anwar and J. Pečarić, Cauchy means of Mercer's type, Utilitas Mathematica, 84, pp. 201-208, 2011.

P.S. Bullen, D.S. Mitrinović and P.M. Vasić, Means and Their Inequalities, Reidel, Dordrecht, 1988. https://doi.org/10.1007/978-94-017-2226-1 DOI: https://doi.org/10.1007/978-94-017-2226-1

W.S. Cheung, A. Matković and J. Pečarić, A variant of Jessen's inequality and generalized means, JIPAM, 7(1), Article 10, 2006.

S.S. Dragomir, A new refinement of Jensen's inequality in linear spaces with applications, Mathematical and Computer Modelling, 52, pp. 1497-1505, 2010. https://doi.org/10.1016/j.mcm.2010.05.035 DOI: https://doi.org/10.1016/j.mcm.2010.05.035

J. Jakšetić and J. Pečarić, Exponential Convexity Method, J. Convex Anal., to appear.

A.W. Marshall, I. Olkin and B.C. Arnold, Inequalities: Theory of majorization and its applications (Second Edition), Springer Series in Statistics, New York 2011. DOI: https://doi.org/10.1007/978-0-387-68276-1

A. Matković and J. Pečarić, Refinements of the Jensen-Mercer inequality for index set functions with applications, Revue d'analyse numérique et de théorie de l'approximation, 35, no. 1, pp. 71-82, 2006, http://ictp.acad.ro/jnaat/journal/article/view/2006-vol35-no1-art10

A.McD. Mercer, A variant of Jensen's inequality, J. Ineq. Pure and Appl. Math., 4(4), 2003, Article 73.

M. Niezgoda, A generalization of Mercer's result on convex functions, Nonlinear Anal., 71, pp. 2771-2779, 2009. https://doi.org/10.1016/j.na.2009.01.120 DOI: https://doi.org/10.1016/j.na.2009.01.120

J. Pečarić and J. Perić, Improvement of the Giaccardi and the Petrović inequality and related Stolarsky type means, An. Univ. Craiova Ser. Mat. Inform., to appear.

J. Pečarić, F. Proschan and Y.L. Tong, Convex functions, Partial Orderings and Statistical Applications, Academic Press, New York, 1992.

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Published

2012-01-01

How to Cite

Khan, M. A., Khan, A. R., & Pečarić, J. (2012). On the refinements of Jensen Mercer’s inequality. Rev. Anal. Numér. Théor. Approx., 41(1), 62–81. https://doi.org/10.33993/jnaat411-969

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