Cauchy-type means for positive linear functionals

Authors

  • 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

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

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.

References

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Published

2011-12-31

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

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Papers