Existence and uniquness theorems for a certain class of non linear singular integral equations

Abstract

In this study, the existence of solution of the non-linear singular integral equation system w(z)f_1(z,w(z),h(z),T_Gg_1(.,w(.),h(.)))(z) h(z)f_2(z,w)(z),h(z),prod_G g_2(,.W(.),h(.)))(Z)' which is more general than the problem partial_zw F(z,w,partial_zw) Rew _{partial G}g(z),g in C{alpha} (partial G) Imw(z_0)c_0,z_0 in overline{G} which has been studied by Ishak Altun , Kerin Koca and Binali Musayev, has been investigated by the same method. Here, T_Gf(z) and prod_Gf(z) are Vekua integral operators defined by T_Gf(z) - frac{1}{pi} int int_G frac{f(zeta)}{zeta - z}d xi d eta prod_G f(z) - frac{1}{pi} int int_G frac{f(zeta)}{(zeta - z)2}d xi d eta