Gibbs phenomenon near irregular initial data points is widely known fact in curve generating by interpolating subdivision schemes. We have recently introduced a class of 3-point nonlinear ternary interpolatingsubdivisionschemes,whicheliminatesGibbs phenomenon or oscillations. In this article, we provide convergence analysis of our class of 3-point nonlinear ternary interpolating subdivision schemes and prove that it is  continuous. Numerical results are presented to support our claim.

interpolating subdivision scheme, Gibbs phenomenon, convergence, smoothness, nonlinear subdivision scheme, oscillatory limit curve.