A Note on the Measure of Solvability
Copyright policy )A Note on the Measure of Solvability
The authors obtain the existence of an \((\alpha)(1+\epsilon)\)-set contraction having a positive minimal displacement. They improve a result obtained by \textit{M.\,Väth} [``Volterra and integral equations of vector functions'' (Pure and Applied Mathematics 224, Marcel Dekker, New York) (2000; Zbl 0940.45002)] stating the existence of a fixed point free mapping \(F\) of the unit ball whose measure of noncompactness is bounded by~\(2\). As applications, they show that the measure of solvability \(\nu(I)\) of the identity operator in any infinite-dimensional Banach space is equal to~\(1\).
- University of Palermo Italy
- University of Calabria Italy
Fixed-point theorems, \((\psi)k\)-set contraction, measure of noncompactness, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., minimal displacement, measure of solvability
Fixed-point theorems, \((\psi)k\)-set contraction, measure of noncompactness, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., minimal displacement, measure of solvability
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