Fixed-point theory on a Frechet topological vector space.
Some fixed point theorems and existence of weak solutions of Volterra integral equation under Henstock-Kurzweil-Pettis integrability
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
In this paper we prove a collection of new fixed point theorems for operators of the form on an unbounded closed convex subset of a Hausdorff topological vector space . We also introduce the concept of demi--compact operator and -semi-closed operator at the origin. Moreover, a series of new fixed point theorems of Krasnosel’skii type is proved for the sum of two operators, where is -sequentially continuous and -compact while is -sequentially continuous (and -condensing, -nonexpansive...
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