当开始新的部分时,我面临额外的间距。
\documentclass[10pt]{report}
\usepackage{mathptmx,amsmath,amssymb,bm}
\begin{document}
\begin{align*}
& \kappa(ru+m(1-r)v)\leq\,r\kappa(u)+m(1-r)\kappa(v)\\
\begin{split}
& \chi\big[\kappa(ru+m(1-r)v)\big]\leq\,\chi\big[r\kappa(u)\\
&+m(1-r)\kappa(v)\big]
\end{split}
\\[2ex]
\begin{split}
& \big(\chi o \kappa\big)\big(ru+m(1-r)v\big)\leq\,h(r) \chi \big[\kappa(u)\big]\\
&+mh(1-r)\varphi\big(\chi \big[\kappa(u)\big],\chi \big[\kappa(v)\big]\big)
\end{split}
\\[2ex]
\begin{split}
& \big(\chi o \kappa\big)\big(ru+m(1-r)v\big)\leq\,h(r)\big(\chi o \kappa\big)(u)\\
&+mh(1-r)\varphi\big((\chi o \kappa)(u),(\chi o \kappa)(v)\big).
\end{split}
\\[2ex]
\end{align*}
\section{Hermite-Hadamard type inequalities.}
The incoming theorems follow ideas from [1]\\
The follwing theorem gives boundedness of $\varphi_{(h,m)}-$convex function and will be use in theorem (4)
Consider $\kappa:I\rightarrow \mathbb{R}$ be $\varphi_{(h,m)}-$convex function, such that $\varphi$ is bounded from above on $\kappa(I)\times \kappa(I)$, then for $p,q\in I$ with $p<q$, $\kappa$ is bounded on $[p,q]\subseteq I$.
\end{document}
答案1
可能与主题无关,但无论如何......
目前尚不清楚,为什么您要使用split
内部align+
环境,而您的方程式可以在没有它的情况下很好地适合页面(即使您对它们进行编号):
\documentclass[10pt]{report}
\usepackage{mathptmx,amsmath,amssymb,bm}
\usepackage{amssymb,mathtools}
\begin{document}
\begin{align*}
\kappa(ru+m(1-r)v)
& \leq\,r\kappa(u) + m(1-r)\kappa(v) \\
\chi\big[\kappa(ru+m(1-r)v)\big]
& \leq\,\chi\big[r\kappa(u) + m(1-r)\kappa(v)\big] \\
\big(\chi o \kappa\big)\big(ru+m(1-r)v\big)
& \leq\,h(r) \chi \big[\kappa(u)\big] + mh(1-r)\varphi\big(\chi\big[\kappa(u)\big],\chi \big[\kappa(v)\big]\big) \\
\big(\chi o \kappa\big)\big(ru+m(1-r)v\big)
& \leq\,h(r)\big(\chi o \kappa\big)(u)+ mh(1-r)\varphi\big((\chi o \kappa)(u),(\chi o \kappa)(v)\big).
\end{align*}
Numbered as subequations:
\begin{subequations}
\begin{align}
\kappa(ru+m(1-r)v)
& \leq\,r\kappa(u) + m(1-r)\kappa(v) \\
\chi\big[\kappa(ru+m(1-r)v)\big]
& \leq\,\chi\big[r\kappa(u) + m(1-r)\kappa(v)\big] \\
\big(\chi o \kappa\big)\big(ru+m(1-r)v\big)
& \leq\,h(r) \chi \big[\kappa(u)\big] + mh(1-r)\varphi\big(\chi\big[\kappa(u)\big],\chi \big[\kappa(v)\big]\big) \\
\big(\chi o \kappa\big)\big(ru+m(1-r)v\big)
& \leq\,h(r)\big(\chi o \kappa\big)(u)+ mh(1-r)\varphi\big((\chi o \kappa)(u),(\chi o \kappa)(v)\big).
\end{align}
\end{subequations}
\section{Hermite-Hadamard type inequalities.}
The incoming theorems follow ideas from [1].
The follwing theorem gives boundedness of $\varphi_{(h,m)}-$convex function and will be use in theorem (4). Consider $\kappa:I\rightarrow \mathbb{R}$ be $\varphi_{(h,m)}$-convex function, such that $\varphi$ is bounded from above on $\kappa(I)\times \kappa(I)$, then for $p,q\in I$ with $p<q$, $\kappa$ is bounded on $[p,q]\subseteq I$.
\end{document}
答案2
我看不出有什么理由split
。
需要注意几点。
\big
在大多数地方是不必要的,应该要么\bigl
或要么\bigr
用于打开和关闭2ex
确实太大了\chi o \kappa
是错误的,应该\chi \circ \kappa
$\varphi_{(h,m)}-$convex
是错误的,应该是$\varphi_{(h,m)}$-convex
;如果你真的想要一个破折号而不是连字符,请使用$\varphi_{(h,m)}$--convex
mathptmx
是一个受人尊敬的 25 岁黑客,但它并不是现在获得 Times 字体的最佳方式显示可能与≤符号对齐,也可能与左侧对齐,请自行选择
使用明确的交叉引用并不是最好的方法,可以在任何 LaTeX 指南中
\label
查找\ref
不要使用
\\
命令来结束段落,而是留一个空行
\documentclass[10pt]{report}
\usepackage{newtxtext,newtxmath}
\usepackage{amsmath}
%\usepackage{amssymb}% not with newtxmath
\usepackage{bm}
\begin{document}
The display with alignment at $\leq$
\begin{align*}
\kappa(ru+m(1-r)v)&\leq r\kappa(u)+m(1-r)\kappa(v)
\\[1ex]
\chi[\kappa(ru+m(1-r)v)]&\leq\chi[r\kappa(u)+m(1-r)\kappa(v)]
\\[1ex]
(\chi \circ \kappa)(ru+m(1-r)v)&\leq h(r) \chi [\kappa(u)]
+mh(1-r)\varphi\bigl(\chi [\kappa(u)],\chi [\kappa(v)]\bigr)
\\[1ex]
(\chi \circ \kappa)(ru+m(1-r)v)&\leq h(r)(\chi \circ \kappa)(u)
+mh(1-r)\varphi\bigl((\chi \circ \kappa)(u),(\chi \circ \kappa)(v)\bigr).
\end{align*}
The display with left alignment
\begin{align*}
& \kappa(ru+m(1-r)v)\leq r\kappa(u)+m(1-r)\kappa(v)
\\[1ex]
& \chi[\kappa(ru+m(1-r)v)]\leq\chi[r\kappa(u)+m(1-r)\kappa(v)]
\\[1ex]
& (\chi \circ \kappa)(ru+m(1-r)v)\leq h(r) \chi [\kappa(u)]
+mh(1-r)\varphi\bigl(\chi [\kappa(u)],\chi [\kappa(v)]\bigr)
\\[1ex]
& (\chi \circ \kappa)(ru+m(1-r)v)\leq h(r)(\chi \circ \kappa)(u)
+mh(1-r)\varphi\bigl((\chi \circ \kappa)(u),(\chi \circ \kappa)(v)\bigr).
\end{align*}
\section{Hermite-Hadamard type inequalities.}
The incoming theorems follow ideas from [1].
The following theorem gives boundedness of $\varphi_{(h,m)}$-convex function
and will be used in theorem~(4).
Consider $\kappa:I\rightarrow \mathbb{R}$ be $\varphi_{(h,m)}$-convex
function, such that $\varphi$ is bounded from above on $\kappa(I)\times \kappa(I)$,
then for $p,q\in I$ with $p<q$, $\kappa$ is bounded on $[p,q]\subseteq I$.
\end{document}