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Applications of Quasiconvexity

In: Contributions in Mathematics and Engineering

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  • S. Abramovich

    (University of Haifa, Department of Mathematics)

Abstract

This survey deals with functions called γ-quasiconvex functions and their relations to convexity and superquadracity. For γ-quasiconvex functions and for superquadratic functions, we get analogs of inequalities satisfied by convex functions and we get refinements for those convex functions which are also γ-quasiconvex as well as superquadratic. We show in which cases the refinements by γ-quasiconvex functions are better than those obtained by superquadratic functions and convex functions. The power functions defined on x ≥ 0 where the power is greater or equal to two are examples of convex, quasiconvex, and superquadratic functions.

Suggested Citation

  • S. Abramovich, 2016. "Applications of Quasiconvexity," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Contributions in Mathematics and Engineering, pages 1-23, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31317-7_1
    DOI: 10.1007/978-3-319-31317-7_1
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