Sufficient conditions for the minimality of biconcave functions

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2023-11-09 DOI:10.1090/spmj/1781

M. Novikov

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引用次数: 1

Abstract

This paper describes sufficient conditions under which a biconcave function B : S = { ( x , y ) ∈ R 2 : x − 2 ≤ y ≤ x + 2 } → R \mathcal {B}\colon \mathfrak {S}=\{ (x,y)\in \mathbb {R}^2\colon x-2\le y\le x+2 \}\to \mathbb {R} is minimal with respect to an obstacle L : S → [ − ∞ , + ∞ ) L\colon \mathfrak {S}\to [-\infty ,+\infty ) , that is, it is the pointwise minimal among all biconcave functions B : S → R B\colon \mathfrak {S}\to \mathbb {R} that satisfy the inequality B ≥ L B\ge L .

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双凹函数极小性的充分条件

本文给出了双凹函数B: S =的充分条件 { (x, y)∈r2: x−2≤y≤x + 2 } →r \mathcal {b}\colon \mathfrak {s}=｛(x,y)\in \mathbb {r}^2\colon x-2\le y\le X +2｝\to \mathbb {r} S→[−∞，+∞)L\colon \mathfrak {s}\to [-]\infty ，+\infty )，即它是所有双凹函数B: S→R B中的点极小值\colon \mathfrak {s}\to \mathbb {r} 满足不等式B≥L B\ge L。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.