Recently, Kanas and Wiśniowska [7, 8, 9] introduced the class of $k$-uniformly convex, and related class of $k$-starlike functions ($0 \le k < \infty$), denoted $\ku$ and $\ks$, respectively. In the present paper a notion of generalized convexity, by applying the well known Ruscheweyh derivative, is introduced. Some extremal problems for functions satisfying the condition of generalized convexity are solved.