In this paper, we introduce the notion of convex -iterated function system (convex(n, m)-IFS). The existence and uniqueness of a fixed point for the Hutchinson map corresponding to a convex (n, m)-IFS has been proved. Also, an extension of the collage theorem for the IFS consisting of convex contractions and the convex (n, m)-IFS are obtained. We are bringing together the ideas in IFS consisting of convex contractions and (n, m)-IFS to obtain a generalization to both. It is shown that the space Conv_a,b(X) of convex contractions on a complete metric space X with convexity parameters a, b is complete, and so is the finite product space [Conv_a,b(X)]ⁿ The continuity of the fixed point map on Conv_a,b(X) is also established towards the end.

Hausdorff metric, convex contraction, (n, m)-IFS, fractal.