In this chapter we review a class of contraction conditions, which are largely used to obtain interesting generalizations of the Banach fixed-point theorem in various abstract settings. We also present a new fixed-point existence result obtained by considering such a kind of contraction condition and a measure of noncompactness. Moreover, we show the applicability of these results in the theory of functional equations.
Vetro, C., Vetro, F. (2017). The class of F-contraction mappings with a measure of noncompactness. In Banas Jozef, Jleli Mohamed, Mursaleen Mohammad, Samet Bessem, Vetro Calogero (a cura di), Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness (pp. 297-331). Springer Singapore [10.1007/978-981-10-3722-1_7].
The class of F-contraction mappings with a measure of noncompactness
Vetro, Calogero;Vetro, Francesca
2017-01-01
Abstract
In this chapter we review a class of contraction conditions, which are largely used to obtain interesting generalizations of the Banach fixed-point theorem in various abstract settings. We also present a new fixed-point existence result obtained by considering such a kind of contraction condition and a measure of noncompactness. Moreover, we show the applicability of these results in the theory of functional equations.
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