摘要
本文研究了Banach空间上的凸泛函四重不等式,该不等式联系于Banach空间中的凸泛函的几何性质及凸函数的光滑性条件.具体地,研究了凸函数f满足一定条件下的单调性和凹凸性,并在1≤p≤2时的p一致光滑Banach空间上,建立了四重不等式,即对任意y,z,k,w∈X,有f(‖y-k‖)+f(‖z-w‖)≤f(‖y-w‖)+f(‖w-k‖)+Cf(‖z-k‖)+Cf(‖y-z‖).并且给出了该结论在L_(p)空间和非交换的L_(p)空间以及某些内插空间上的应用.这一工作是Enflo关于圆度不等式及Schotz在Hilbert空间上的凸泛函四重不等式在Banach空间框架下的推广.
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 functionals within Banach spaces and the smoothness conditions of convex functions.Speciflcally,we explore the monotonicity and concavity-convexity of the convex function f under speciflc conditions.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‖)+Cf(‖y-z‖)Furthermore,we present the applications of this conclusion in L_(p)spaces,non-commutative L_(p)spaces,and certain interpolation spaces.This research represents a generalization of the roundness inequality and Schotz’s quadruple inequality for convex functionals on Hilbert spaces.
作者
谢子秀
马涛
XIE Zi-xiu;MA Tao(School of Mathematics and Statistics,Central South Minzu University,Wuhan 430074,China)
出处
《数学杂志》
2026年第2期86-96,共11页
Journal of Mathematics
基金
国家自然科学基金资助(12071358)。
