数学杂志2026，Vol.46Issue(2)：86-96,11.
Banach空间几何性质与凸泛函四重不等式
GEOMETRIC PROPERTIES OF BANACH SPACES AND THE QUADRUPLE INEQUALITY FOR CONVEX FUNCTIONALS
摘要
Abstract
In this paper,we delve into the quadruple inequality for convex functionals in Banach spaces.This inequality is intricately linked to the geometric characteristics of convex func-tionals within Banach spaces and the smoothness conditions of convex functions.Specifically,we explore the monotonicity and concavity-convexity of the convex function f under specific condi-tions.For a p-uniformly smooth Banach space with 1 ≤ p ≤ 2,we establish a quadruple inequality.Precisely,for any y,z,k,w ∈ X,the following inequality holds:f(‖y-k‖)+f(‖z-w‖)≤ f(‖y-w‖)+f(‖w-k‖)+Cf(‖z-k‖p)+Cf(‖y-z‖).Furthermore,we present the applications of this conclusion in Lp spaces,non-commutative Lp spaces,and certain interpolation spaces.This research represents a generalization of the roundness inequality and Schötz's quadruple inequality for convex functionals on Hilbert spaces.关键词
Banach空间几何/四重不等式/p一致光滑性/Clarkson不等式/凸泛函Key words
The geometry of banach spaces/quadruple inequality/p-uniform smoothness/Clarkson's inequality/Convex functional分类
数理科学引用本文复制引用
谢子秀,马涛..Banach空间几何性质与凸泛函四重不等式[J].数学杂志,2026,46(2):86-96,11.基金项目
国家自然科学基金资助(12071358). （12071358）
