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New Inequalities for η-Quasiconvex Functions

In: Frontiers in Functional Equations and Analytic Inequalities

Author

Listed:
  • Eze R. Nwaeze

    (Alabama State University, Department of Mathematics and Computer Science)

  • Delfim F. M. Torres

    (University of Aveiro, Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics)

Abstract

The class of η-quasiconvex functions was introduced in 2016. Here we establish novel inequalities of Ostrowski type for functions whose second derivative, in absolute value raised to the power q ≥ 1, is η-quasiconvex. Several interesting inequalities are deduced as special cases. Furthermore, we apply our results to the arithmetic, geometric, Harmonic, logarithmic, generalized log and identric means, getting new relations amongst them.

Suggested Citation

  • Eze R. Nwaeze & Delfim F. M. Torres, 2019. "New Inequalities for η-Quasiconvex Functions," Springer Books, in: George A. Anastassiou & John Michael Rassias (ed.), Frontiers in Functional Equations and Analytic Inequalities, pages 423-434, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-28950-8_22
    DOI: 10.1007/978-3-030-28950-8_22
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