Step method for a system of integral equations from biomathematics

Keywords: System of nonlinear integral equations Step method Picard operators Generalized fibre contraction principle a b s t r a c t Using the step method, we study the following system of integral equations from biomathematics xðtÞ ¼ gðt; xðtÞ; xðt À sÞÞ þ Z t tÀs f ðs; xðsÞÞds; t 2 ½a; bŠ; s > 0 and we prove the existence, uniqueness and the convergence of the successive approximation sequence using the Perov contraction principle and step method with a weaker Lips-chitz 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.