Upper bound for the first non-zero eigenvalue of the $p$-Laplacian

Let $M$ be a closed hypersurface in ${\mathbb{R}}^n$ and $\mathrm{\Omega }$ be a bounded domain such that $M=\mathrm{\partial }\mathrm{\Omega }$. 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}