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.
|Title of host publication
|Contributions in Mathematics and Engineering
|Subtitle of host publication
|In Honor of Constantin Caratheodory
|Springer International Publishing
|Number of pages
|Published - 1 Jan 2016
Bibliographical notePublisher Copyright:
© Springer International Publishing Switzerland 2016.
ASJC Scopus subject areas
- General Mathematics