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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.
MSC:
 45G10 Nonsingular nonlinear integral equations 47H08 Measures of noncompactness and condensing mappings, $K$-set contractions, etc. 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 47N20 Applications of operator theory to differential and integral equations