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Note on measures of noncompactness in Banach sequence spaces.

Jozef BanasAntonio Martinón — 1990

Extracta Mathematicae

The notion of a measure of noncompactness turns out to be a very important and useful tool in many branches of mathematical analysis. The current state of this theory and its applications are presented in the books [1,4,11] for example. The notion of a measure of weak noncompactness was introduced by De Blasi [8] and was subsequently used in numerous branches of functional analysis and the theory of differential and integral equations (cf. [2,3,9,10,11], for instance). In...

Deformation of Banach spaces

Józef BanaśKrzysztof Fraczek — 1993

Commentationes Mathematicae Universitatis Carolinae

Using some moduli of convexity and smoothness we introduce a function which allows us to measure the deformation of Banach spaces. A few properties of this function are derived and its applicability in the geometric theory of Banach spaces is indicated.

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

Józef BanaśAfif 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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