The paper presents results concerning the solvability of a nonlinear integral equation of Volterra-Stieltjes type. We show that under some assumptions that equation has a continuous and bounded solution defined on the interval0,∞and having a finite limit at infinity. As a special case of the mentioned integral equation we obtain an integral equation of Volterra-Wiener-Hopf type. That fact enables us to formulate convenient and handy conditions ensuring the solvability of the equation in question in the class of functions defined and continuous on the interval0,∞and having finite limits at infinity.

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We conduct some investigations concerning the solvability of a nonlinear integral equation of Erdélyi-Kober type. To facilitate our study we will first consider a nonlinear integral equation of Volterra-Stieltjes type. Since the mentioned Erdélyi-Kober integral equation turns out to be a special case of that of Volterra-Stieltjes type, we can apply the obtained results to the Erdélyi-Kober integral equation. Examples illustrating the obtained results will be also included.

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