Displaying similar documents to “On the Volterra integral equation and the Henstock-Kurzweil integral.”

Linear Volterra-Stieltjes integral equations in the sense of the Kurzweil-Henstock integral

Márcia Federson, Ricardo Bianconi (2001)

Archivum Mathematicum

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In 1990, Hönig proved that the linear Volterra integral equation x t - ( K ) ∫ a , t α t , s x s d s = f t , t ∈ a , b , where the functions are Banach space-valued and f is a Kurzweil integrable function defined on a compact interval a , b of the real line ℝ , admits one and only one solution in the space of the Kurzweil integrable functions with resolvent given by the Neumann series. In the present paper, we extend Hönig’s result to the linear Volterra-Stieltjes integral equation x t - ( K ) ∫ a , t α t , s x s d g s = f t , t ∈ a , b , in a real-valued context.

Some fixed point theorems and existence of weak solutions of Volterra integral equation under Henstock-Kurzweil-Pettis integrability

Afif Ben Amar (2011)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we examine the set of weakly continuous solutions for a Volterra integral equation in Henstock-Kurzweil-Pettis integrability settings. Our result extends those obtained in several kinds of integrability settings. Besides, we prove some new fixed point theorems for function spaces relative to the weak topology which are basic in our considerations and comprise the theory of differential and integral equations in Banach spaces.