AUTHOR(S): Adeeb G. Talafha, Feras Al Faqih, Iurie Caraus

TITLE 
ABSTRACT The main propose of this research is the investigation and theoretical background of the directapproximate methods for the numerical solution of singular integral equations with translation and conjugation of the unknown function defined on the smooth contours of the Lyapunov type. The equations are defined on the system of Fej´er points. The numerical schemes of collocation and mechanical quadrature methods for the equations with conjugations of the unknown function and for the equations with translation are elaborated. This problem has been well studied for the case of functions defined on standard contours (a straight line segment, the unit circle, and so on). In the case of an arbitrary closed smooth contour in the complex plane, the problem is not studied enough. We suggest the numerical schemes of the Lagrange interpolation polynomials for the approximate solution of weakly SIE defined on smooth closed contours in the complex plane. Our approach is based on the Zolotarevski theory. The theorems of convergence for research methods are proved in Generalized H¨older spaces. 
KEYWORDS Singular Integral Equations, Fej´er points, Generalized H¨older spaces, Collocation Methods, Mechanical_x000D_ 

Cite this paper Adeeb G. Talafha, Feras Al Faqih, Iurie Caraus. (2019) DirectApproximateMethods for Solution of Singular Integral Equations with Complex Conjugation Defined on the System of Fejer Points on Contour G in Generalized Holder Spaces. International Journal of Mathematical and Computational Methods, 4, 2330 
