  Let $M$ be a closed hypersurface in $\mathbb{R}^{n}$ and $\Omega$ be a
bounded domain such that $M= \partial\Omega$. In this article, we obtain an
upper bound for the first non-zero eigenvalue of the following problems.
  \begin{itemize} \item Closed eigenvalue problem: \begin{align*}
%\label{eqn:closedep} \Delta_p u = \lambda_{p} \ |u|^{p-2} \ u \qquad \mbox{ on
} \quad {M}. \end{align*} \item Steklov eigenvalue problem:
  \begin{align*} \begin{array}{rcll}
  \Delta_{p}u &=& 0 & \mbox{ in } \Omega ,\\ |\nabla u|^{p-2} \frac{\partial
u}{\partial \nu} &=& \mu_{p} \ |u|^{p-2} \ u &\mbox{ on } M . \end{array}
\end{align*} \end{itemize}
