Cauchy-type means for positive linear functionals

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Published: Dec 31, 2011
DOI: https://doi.org/10.5556/j.tkjm.42.2011.1036
Keywords:
Jensen’s inequality Mean-value theorems Linear functional means Generalized means Generalized powermean Cauchy-type means

Main Article Content

M. Anwar
Center for AdvancedMathematics and Physics, NationalUniversity of Sciences and Technology, Islamabad, Pakistan.
J. Pecaric
Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovi´ca 28a, 10000 Zagreb, Croatia. Abdus SalamSchool of Mathematical Sciences, GC University, Lahore, Pakistan.
M. Rodi´c Lipanovi´c
Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovi´ca 28a, 10000 Zagreb, Croatia

Abstract

Some mean-value theorems of the Cauchy type, which are connected with Jensen's inequality, are given in \cite{Mercer2} in discrete form and in \cite{PPSri} in integral form. Here we give the generalization of that result for positive linear functionals. Using that result, new means of Cauchy type for positive linear functionals are given. Monotonicity of these new means is also discussed.

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How to Cite
Anwar, M., Pecaric, J., & Lipanovi´c, M. R. (2011). Cauchy-type means for positive linear functionals. Tamkang Journal of Mathematics, 42(4), 511–530. https://doi.org/10.5556/j.tkjm.42.2011.1036
Issue
Vol. 42 No. 4 (2011)
Section
Papers

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