The purpose of this paper is to define a newclass of analytic, normalizedfunctions in the open unit disk $\Delta=\{ z:z\in \mathbb{C}\quad \text{and}\quad \left\vertz\right\vert <1\}$ subordinating with crescent shaped regions, and to derive certain coefficient estimates $a_2$ , $a_3$ and Fekete-Szeg\{o} inequality for $f\in\mathscr{M}_q(\alpha,\beta,\lambda)$. A similar result have been done for the function $ f^{-1}. $ Further application of our results to certain functions defined by convolution products with a normalizedanalytic function is given, in particular we obtainFekete-Szeg\{o} inequalities for certainsubclasses of functions defined through Poisson distribution series.