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Zbl 1228.45002
Aghajani, Asadollah; Banaś, Józef; Jalilian, Yaghoub
Existence of solutions for a class of nonlinear Volterra singular integral equations. (English)
[J] Comput. Math. Appl. 62, No. 3, 1215-1227 (2011). ISSN 0898-1221

Summary: We prove some results concerning the existence of solutions for a large class of nonlinear Volterra singular integral equations in the space $C[0,1]$ consisting of real functions defined and continuous on the interval $[0,1]$. The main tool used in the proof is the concept of a measure of noncompactness. We also present some examples of nonlinear singular integral equations of Volterra type to show the efficiency of our results. Moreover, we compare our theory with the approach depending on the use of the theory of Volterra-Stieltjes integral equations. We also show that the results of the paper are applicable in the study of the so-called fractional integral equations which are recently intensively investigated and find numerous applications in describing some real world problems.

MSC 2000:: *45D05 Volterra integral equations

Keywords: Volterra singular integral equation; measure of noncompactness; fixed point theorem; function of bounded variation; integral equation of Volterra; Stieltjes type

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