On a weakly singular quadratic integral equations of Volterra type in Banach algebras. (English) Zbl 1343.45003
Summary: In this paper, we present existence and uniqueness theorems of nonnegative, asymptotically stable, and ultimately nondecreasing solutions for weakly singular quadratic integral equations of Volterra type in Banach algebras. The concept of the measure of noncompactness and a fixed point theorem due to Darbo acting in a Banach algebra are the main tools in carrying out our proof. An effective numerical example is given to illustrate our theory results.
MSC:
| 45G05 | Singular nonlinear integral equations |
| 47H30 | Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) |
Keywords:
weakly singular quadratic integral equations; Banach algebras; measure of noncompactness; fixed point theoremReferences:
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