Existence of solutions for a class of nonlinear Volterra singular integral equations

In this paper 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 m...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2011-08, Vol.62 (3), p.1215-1227
Main Authors: Aghajani, Asadollah, Banaś, Józef, Jalilian, Yaghoub
Format: Article
Language:English
Subjects:
Fixed point theorem
Function of bounded variation
Integral equation of Volterra–Stieltjes type
Integral equations
Intervals
Mathematical analysis
Mathematical models
Measure of noncompactness
Nonlinearity
Proving
Singular integral equations
Volterra singular integral equation
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Summary:In this paper 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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2011.03.049