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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

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.

Measures of noncompactness in locally convex spaces and fixed point theory for the sum of two operators on unbounded convex sets

Józef Banaś;  Afif Ben Amar — 2013

Commentationes Mathematicae Universitatis Carolinae

In this paper we prove a collection of new fixed point theorems for operators of the form T + S on an unbounded closed convex subset of a Hausdorff topological vector space ( E , Γ ) . We also introduce the concept of demi- τ -compact operator and τ -semi-closed operator at the origin. Moreover, a series of new fixed point theorems of Krasnosel’skii type is proved for the sum T + S of two operators, where T is τ -sequentially continuous and τ -compact while S is τ -sequentially continuous (and Φ τ -condensing, Φ τ -nonexpansive...

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