| Citation: |
Shu-Hong Wang, Qian Liu, Feng Qi. ON p-GEOMETRICALLY CONVEX SETS AND FUNCTIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1963-1977. doi: 10.11948/20250055
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ON p-GEOMETRICALLY CONVEX SETS AND FUNCTIONS
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Abstract
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 $-geometrically convex functions.
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References
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Shu-Hong Wang, Qian Liu, Feng Qi. ON p-GEOMETRICALLY CONVEX SETS AND FUNCTIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1963-1977. doi: 10.11948/20250055
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$ p $ $ U=\bigl\{\bigl(1/2^\lambda,1/2^\mu\bigr):\lambda,\mu\in[0,1],\lambda^p+\mu^p=1\bigr\} $