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Abstract and Applied Analysis
Volume 2014, Article ID 982079, 9 pages
Research Article

Solvability of an Integral Equation of Volterra-Wiener-Hopf Type

1Department of Mathematics, Science-Pedagogical Faculty, M. Auezov South Kazakhstan State University, Tauke Khan Avenue 5, Shymkent 160012, Kazakhstan
2Department of Mathematics, Rzeszów University of Technology, Al. Powstanców Warszawy 8, 35-359 Rzeszów, Poland

Received 10 March 2014; Accepted 1 May 2014; Published 13 May 2014

Academic Editor: Xiao-Jun Yang

Copyright © 2014 Nurgali K. Ashirbayev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 interval 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 interval and having finite limits at infinity.