Double tagged equations?

Question

In the following example

the inequality (2.26) is obtained in the environment equation, but the equations (2.27) and (2.28) by dirty tricks, destroying the structure of the document. This is because additional tags (i) and (ii) are needed on the left-hand side of lines. (This is, in fact, some kind of an enumeration).

How to obtain such additional tags in equations or even more: produce a list with equations of its elements?

I am trying to find better solutions then How to number equations with a list environment

Remark. According to some wishes a (very ugly) code snippet. I hope that it would be enough instead of MWE and I know, that one should not use LaTeX in the presented way.

Indukcja matematyczna pozwala przenieść nierówność \eqref{(2.25)} na dowolną liczbę składników:
\begin{equation}
\label{(2.26)}
 J(X_1+\ldots +X_n)\leqslant \alpha_1^2J(X_1)+\ldots +\alpha_n^2J(X_n),%$ \hfill (2.26) 
\end{equation}

\vspace{2mm}
\noindent gdzie $X_1,\ldots ,X_n$ są niezależne oraz $\alpha_i\in[0,1],\; \sum_{i=1}^n\alpha_i=1$. Nierówność (2.26) udowodnili Stam (1959) oraz Blachman (1965), nie korzystając z lematu 2.2. Nierówność (2.26) można zapisać w kilku 
równoważnych postaciach:

\vspace{2mm}
\noindent$\;\;${\it (i) $\;\;\;J(\sqrt{\alpha_1}X_1+\ldots +\sqrt{\alpha_n}X_n)\leqslant \alpha_1J(X_1)+\ldots +\alpha_nJ(X_n)$;\hfill {\rm (2.27)}

\vspace{2mm}
\noindent$\;\;$(ii) $\;\;\displaystyle \frac{1}{J(X_1+\ldots +X_n)}\geqslant \frac{1}{J(X_1)}+\ldots +\frac{1}{J(X_n)}$;\hfill
{\rm (2.28)}

Answer 1

EDIT

I decided that I didn't really like my first solution (see below) because it requires all of this "extra clutter" in order for it to work. So, I have written a custom enumitem environment equationate (=equation+enumerate) that does the same thing except that it hides the clutter inside the environment.

The output is given above, which is exactly the same as for my first solution, but the input now only requires some equations inside an enumerate-like environment. These equations are automatically typeset as mathematics in \displaystyle. Even though it doesn't look like it above (I shrunk the image), the equation numbers are flush with the righthand margin.

Here is the new MWE:

\documentclass{article}
\usepackage{enumitem}
\usepackage[width=80mm]{geometry}

\renewcommand\theequation{(\arabic{section}.\arabic{equation})}

\let\realItem=\item
\newcommand\EquationItem[1][\relax]{%
  \ifmmode\EndEquationItem\fi% close off math-mode from last item
  \ifx\relax#1\relax\realItem\else\realItem[#1]\fi%
  \refstepcounter{equation}$\displaystyle%
}
\newcommand\EndEquationItem{$\hfill\theequation}
\newlist{equationate}{enumerate}{1}
\setlist[equationate]{label=\roman*), before=\global\let\item\EquationItem,
                      after=\EndEquationItem\global\let\item\realItem}

\begin{document}
\section{Some equations}

  \begin{equationate}
    \item \sum_{k=1}^nk=\frac12 n(n+1)
    \item \sum_{k=1}^nk^2=\frac16n(n+1)(2n+1)
  \end{equationate}

\end{document}

Notice that because equationate is an enumitem environment you can customise it on the fly in the usual way. For example,

  \begin{equationate}[label=\alph*)]
    \item \sum_{k=1}^nk=\frac12 n(n+1)
    \item \sum_{k=1}^nk^2=\frac16n(n+1)(2n+1)
  \end{equationate}

will print the item numbers as a), b), .... Of course, if you change the values of before or after then everything will break. If you're keen it shouldn't be hard to add an option so that \item* suppresses the equation label for an item.

Original solution

I would use the following (using the enumitem package):

\documentclass{article}
\usepackage{enumitem}
\usepackage[width=80mm]{geometry}
\begin{document}
  \section{Some equations}
  \renewcommand\theequation{(\arabic{section}.\arabic{equation})}

    \begin{enumerate}[label=\roman*)]
      \item $\displaystyle \sum_{k=1}^nk=\frac12 n(n+1)$
      \refstepcounter{equation}\hfill\theequation
      \item $\displaystyle \sum_{k=1}^nk^2=\frac16n(n+1)(2n+1)$
      \refstepcounter{equation}\hfill\theequation
    \end{enumerate}

\end{document}

This is not much of hack and it produces the image above.

Answer 2

Wouldn't it be the easiest way to use an align or alignat here? I replaced the \ldots by \dots in between the binary operators as they are looking wrong.

% arara: pdflatex

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathtools}
\usepackage{amssymb}
\renewcommand\theequation{\arabic{section}.\arabic{equation}}

\begin{document}
    \setcounter{section}{2} 
    \setcounter{equation}{25}
    Indukcja matematyczna pozwala przenieść nierówność (2.25) na dowolną liczbę składników:
    \begin{equation}
        \label{(2.26)}
        J(X_1 + \dots + X_n) \leqslant \alpha_1^2J(X_1) + \dots + \alpha_n^2J(X_n),
    \end{equation}
    gdzie $X_1, \dots, X_n$ są niezależne oraz $\alpha_i\in[0,1],\; \sum_{i=1}^n\alpha_i=1$. Nierówność (2.26) udowodnili Stam (1959) oraz Blachman (1965), nie korzystając z lematu 2.2. Nierówność (2.26) można zapisać w kilku 
    równoważnych postaciach:    
    \begin{alignat}{2}
        &(i)\qquad &&J(\sqrt{\alpha_1}X_1+ \dots +\sqrt{\alpha_n}X_n)\leqslant \alpha_1J(X_1)+ \dots +\alpha_nJ(X_n);\\
        &(ii)\qquad &&\displaystyle \frac{1}{J(X_1+ \dots +X_n)}\geqslant \frac{1}{J(X_1)}+ \dots + \frac{1}{J(X_n)};
    \end{alignat}
\end{document}

If you need the left labels flush left, you should go with a table I guess.