Several Jensen–Grüss inequalities with  applications in information theory

S. I.  Butt; Ð.  Pečarić; J.  Pečarić

doi:10.37863/umzh.v74i12.6554

S. I. Butt COMSATS Univ. Islamabad, Lahore Campus, Pakistan https://orcid.org/0000-0001-7192-8269
Ð. Pečarić Catholic Univ. Croatia, Zagreb
J. Pečarić Catholic Univ. Croatia, Zagreb

DOI: https://doi.org/10.37863/umzh.v74i12.6554

Keywords: Jensen difference, Gr\

Abstract

UDC 517.5

Several integral Jensen–Grüss inequalities are proved together with their refinements. Some new bounds for integral Jensen–Chebyshev inequality are obtained. The multidimensional integral variants are also presented. In addition, some integral Jensen–Grüss inequalities for monotone and completely monotone functions are established. Finally, as an application, we present the refinements for Shannon's entropy.

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