On construction of approximate solutions of nonlinear Volterra-Fredholm integral equation in the space \(L_ p\) (\(p\geq 1\)) (Q2367648)

The authors propose a method for finding an approximate solution of mixed additive nonlinear Volterra-Fredholm integral equations in the space \(L_ p\) (\(p\geq 1\)). The equation has the form \(y(x)=g(x)+\mu\int^ x_ 0V(x,t)f[t,y(t)]dt+\lambda\int^{2\pi}_ 0F(x,t)y(t)dt\). Using linear polynomial operators, they replace the given equation by a nonlinear integral equation of Hammerstein type with degenerate kernel and take its solution as an approximate solution to the given equation.