Aequationes mathematicae

, Volume 92, Issue 2, pp 289–309 | Cite as

Jensen–Steffensen inequality for diamond integrals, its converse and improvements via Green function and Taylor’s formula

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Abstract

In this paper we define the Jensen–Steffensen inequality and its converse for diamond integrals. Then we give some improvements of these inequalities using Taylor’s formula and the Green function. We investigate bounds for the identities related to improvements of the Jensen–Steffensen inequality and its converse.

Keywords

Diamond integrals Jensen–Steffensen inequality Green function Taylor’s formula 

Mathematics Subject Classification

Primary 26D15 Secondary 39A13 34N05 
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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Lahore (Sargodha Campus)SargodhaPakistan
  2. 2.Department of MathematicsWomen University of Azad Jammu and KashmirBaghPakistan
  3. 3.Faculty of Textile TechnologyUniversity of ZagrebZagrebCroatia

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