Approximation of Complex Functions from Morrey space on Dini smooth Curves

In this work, we have studied the issue of approximation of functions from Morrey space ; by rational functions on a large group of curves, which called Dini-smooth curves. Moreover, approximation of functions from Morrey Smirnov space defined on a finite domain with a boundary belonging to Dini- smooth curves by polynomials is obtained.

Approximation of Complex Functions from Weighted Lebesgue space on Carlson Curves

In this research, we have studied the issue of approximation of complex functions from weighted Lebesgue space ; and (Mukenhoupt weight) to rational functions by using p- Faber polynomials on large group of curves, which called Carlson curves. Thisis also considered as a follow-up to the work done by researchers: Israfilov and Testici in 2014 , where they studied approximation of functions from weighted Smirnov space on domains with a Carlson curve boundary.

Approximation of Complex Functions on some subclass of Carlson Curves

We study in this research approximation of complex functions from Orlicz space on a subclass of Carlson curves, which called Dini smooth curves to rational functions by using polynomials related with Dzjadyk sums which obtained from Faber polynomials. We depend on some concepts of complex analysis such as formulas of Sokhotski to reach the desired goal