Numerical integration with weights of convex functions of algebraic polynomials
The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.
It is well-known that the interpolation theory plays an important role in many fields of computer vision, especially in surface reconstruction. In this paper, we introduce a new kind of 2-period interpolation of functions with period . We find out the necessary and sufficient conditions for regularity of this new interpolation problem. Moreover, a closed form expression for the interpolation polynomial is given. Our interpolation is of practical significance. Our results provide the theoretical...