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Investigation on the existence of solutions for some nonlinear functional-integral equations. (English) Zbl 1238.45004
Summary: We prove an existence theorem for a nonlinear integral equation which is a Volterra counterpart of an integral equation arising in traffic theory. Using the technique of the measure of noncompactness in Banach algebra, we prove an existence theorem for a nonlinear functional-integral equation. Basic fixed point theorems such as Darbo’s theorem are employed to obtain the aforementioned aims in Banach algebra.

45G10Nonsingular nonlinear integral equations
47H08Measures of noncompactness and condensing mappings, $K$-set contractions, etc.
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47N20Applications of operator theory to differential and integral equations
Full Text: DOI
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[11] Guo, D.; Lakshmikantham, V.; Liu, X. Z.: Nonlinear integral equations in abstract spaces. (1996) · Zbl 0866.45004
[12] Banas, J.; Goebel, K.: Measures of noncompactness in Banach spaces. (1980) · Zbl 0441.47056