The geometrically convex function is a generalization of convex functions and a useful tool to discover and prove inequalities. In present paper, the authors improve the concept of geometrically convex sets, define the p -geometrically convex sets, the p -geometrically convex hulls, and the p -geometrically convex combinations, and give several equivalent conditions for judging p -geometrically convex sets. On this basis, the authors introduce the concept of p -geometrically convex functions and study its properties and invariant property under several operations. Moreover, the authors establish some new integral inequalities of p -geometrically convex functions.
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Wang et al. (Thu,) studied this question.
www.synapsesocial.com/papers/69b3aaa802a1e69014ccb7d3 — DOI: https://doi.org/10.11948/20250055
Shu-Hong Wang
Qian Liu
Feng Qi
Journal of Applied Analysis & Computation
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