Step method for a system of integral equations from biomathematics

Using the step method, we study the following system of integral equations from biomathematicsx(t)=g(t,x(t),x(t-τ))+∫t-τtf(s,x(s))ds,t∈[a,b],τ>0and we prove the existence, uniqueness and the convergence of the successive approximation sequence using the Perov contraction principle and step method with a weaker Lipschitz condition. Also, we propose a new algorithm of successive approximation sequence generated by the step method and we give an example to illustrate the applications of the abstract results.