A review of shape preserving approximation methods and algorithms for approximating univariate functions or discrete data is given. The notion of 'shape' refers to the geometrical behavior of a function's or approximant's graph, and usually includes positivity, monotonicity, and/or convexity. But, in the recent literature, the broader concept of shape also includes symmetry, generalized convexity, unimodality, Lipschitz property, possessing peaks or discontinuities, etc. Special stress is put on shape preserving interpolation methods by polynomials and splines. Of course, this text has no pretensions to be complete.
Kocić, L. M., & Milovanović, G. V. (1997). Shape preserving approximations by polynomials and splines. Computers and Mathematics with Applications, 33(11), 59–97. https://doi.org/10.1016/S0898-1221(97)00087-4