  In this paper we define a new subclass $\lambda$-bi-pseudo-starlike functions
of $\Sigma$ related to shell-like curves connected with Fibonacci numbers and
determine the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for
$f\in\mathcal{PSL}_{\Sigma}^\lambda(\tilde{p}(z)).$ Further we determine the
Fekete-Szeg\"{o} result for the function class
$\mathcal{PSL}_{\Sigma}^\lambda(\tilde{p}(z))$ and for special cases,
corollaries are stated which some of them are new and have not been studied so
far.
