  Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^n,
\{\omega_k\}_{k=1}^n)$ be two p-orthonormal bases for a finite dimensional
Banach space $\mathcal{X}$. If $ x \in \mathcal{X}\setminus\{0\}$ is such that
$\theta_fx$ is $\varepsilon$-supported on $M\subseteq \{1,\dots, n\}$ w.r.t.
p-norm and $\theta_gx$ is $\delta$-supported on $N\subseteq \{1,\dots, n\}$
w.r.t. p-norm, then we show that \begin{align}\label{ME} (1) \quad \quad \quad
\quad &o(M)^\frac{1}{p}o(N)^\frac{1}{q}\geq \frac{1}{\displaystyle \max_{1\leq
j,k\leq n}|f_j(\omega_k) |}\max \{1-\varepsilon-\delta, 0\},\\ (2) \quad \quad
\quad \quad&o(M)^\frac{1}{q}o(N)^\frac{1}{p}\geq \frac{1}{\displaystyle
\max_{1\leq j,k\leq n}|g_k(\tau_j) |}\max \{1-\varepsilon-\delta,
0\},\label{ME2} \end{align} where \begin{align*} \theta_f: \mathcal{X} \ni x
\mapsto (f_j(x) )_{j=1}^n \in \ell^p([n]); \quad \theta_g: \mathcal{X} \ni x
\mapsto (g_k(x) )_{k=1}^n \in \ell^p([n]) \end{align*} and $q$ is the conjugate
index of $p$. We call Inequalities (1) and (2) as \textbf{Functional
Donoho-Stark Approximate Support Uncertainty Principle}. Inequalities (1) and
(2) improve the finite approximate support uncertainty principle obtained by
Donoho and Stark \textit{[SIAM J. Appl. Math., 1989]}.
