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Refinements of the majorization-type inequalities via green and fink identities and related results

  • Sadia Khalid EMAIL logo , Josip Pečarić and Ana Vukelić
From the journal Mathematica Slovaca


In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities.

MSC 2010: Primary 26A51; 26D15
  1. Communicated by Ján Borsík


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Received: 2016-09-19
Accepted: 2017-04-11
Published Online: 2018-08-06
Published in Print: 2018-08-28

© 2018 Mathematical Institute Slovak Academy of Sciences

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