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Generalization of Popoviciu-Type Inequalities Via Fink’s Identity

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Abstract

We obtained useful identities via Fink’s identity, by which the inequality of Popoviciu for convex functions is generalized for higher order convex functions. We investigate the bounds for the identities related to the generalization of the Popoviciu inequality using inequalities for the Čebyšev functional. Some results relating to the Grüss- and Ostrowski-type inequalities are constructed. Further, we also construct new families of exponentially convex functions and Cauchy-type means by looking at linear functional associated with the obtained inequalities.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS, Institute of Information Technology, Lahore, Pakistan

    Saad Ihsan Butt

  2. Faculty of Textile Technology, University of Zagreb, 10000, Zagreb, Croatia

    Josip Pečarić

  3. Mathematics Department, Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 10000, Zagreb, Croatia

    Ana Vukelić

Authors
  1. Saad Ihsan Butt
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  2. Josip Pečarić
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  3. Ana Vukelić
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Correspondence to Saad Ihsan Butt.

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Butt, S.I., Pečarić, J. & Vukelić, A. Generalization of Popoviciu-Type Inequalities Via Fink’s Identity. Mediterr. J. Math. 13, 1495–1511 (2016). https://doi.org/10.1007/s00009-015-0573-8

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  • DOI: https://doi.org/10.1007/s00009-015-0573-8

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