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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Lahore (Sargodha Campus), Sargodha, 40100, Pakistan

    Ammara Nosheen

  2. Department of Mathematics, Women University of Azad Jammu and Kashmir, Bagh, Azad Kashmir, Pakistan

    Rabia Bibi

  3. Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10000, Zagreb, Croatia

    Josip Pečarić

Authors
  1. Ammara Nosheen
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  2. Rabia Bibi
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  3. Josip Pečarić
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Correspondence to Ammara Nosheen.

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Nosheen, A., Bibi, R. & Pečarić, J. Jensen–Steffensen inequality for diamond integrals, its converse and improvements via Green function and Taylor’s formula. Aequat. Math. 92, 289–309 (2018). https://doi.org/10.1007/s00010-017-0527-2

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  • DOI: https://doi.org/10.1007/s00010-017-0527-2

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