Recently, Kanas and Ronning introduced the classes of functions starlike and convex, which are normalized with $f(w) = f'(w) - 1 = 0$, $w$ is a fixed point in the open disc $\Delta = \{z \in \mathbb{C} : |z| < 1\}$. The aim of this paper is to continue this investigation and introduce a new class $S T_m^l(\alpha,\beta,w)$ of functions which are analytic in $\Delta$. We obtain various results including coefficients estimates, distortion and covering theorems, radii of close-to-convexity, starlikeness and convexity for functions belonging to this class.