On Solution of A Certain Class of Non Linear Singular Integral Equations

In this study, the existence of solution of the non-linear singular integral equation systemw(z)=f (.,w(.),h(.),T_{G}g (.,w(.),h(.)),∏_{G}h (.,w(.),h(.)))(z) h(z)=f (.,w(.),h(.),T_{G}g (.,w(.),h(.)),∏_{G}h (.,w(.),h(.)))(z)has been investigated. Here,T_{G}f(z)and∏_{G}f(z)are Vekua integral operators defined byT_{G}f(z) = -(1/π) _{G}((f( ))/( -z))dξdη ∏_{G}f(z) = -(1/π) _{G}((f( ))/(( -z)2))dξdη.