Construction of a family of non-stationary combined ternary subdivision schemes reproducing exponential polynomials

In this paper, we propose a family of non-stationary combined ternary (2m + 3)-point subdivision schemes, which possesses the property of generating/reproducing high-order exponential polynomials. This scheme is obtained by adding variable parameters on the generalized ternary subdivision scheme of order 4. For such a scheme, we investigate its support and exponential polynomial generation/reproduction and get that it can generate/reproduce certain exponential polynomials with suitable choices of the parameters and reach 2m + 3 approximation order. Moreover, we discuss its smoothness and show that it can produce C2m+2 limit curves. Several numerical examples are given to show the performance of the schemes.