LAUSR

In this paper, we prove some results concerning the existence and uniqueness of solutions for a large class of nonlinear Volterra integral equations of the second kind, especially singular Volterra integral equations, in the Banach space $$X:=C([0,1])$$X:=C([0,1]) consisting of real functions defined and continuous on the interval [0, 1]. The main idea used in the proof is that by using a new contraction condition we can construct a Cauchy sequence in the complete metric space X such that it is convergent to a unique element of this space. Finally, we present some examples of nonlinear singular integral equations of Volterra type to show the efficiency of our results.