Abstract
AbstractIn this paper, we propose a new idea to investigate the important basic problem: how to extend Darbo’s fixed point theorem? We establish some new generalizations of Darbo’s fixed point theorem by using ‘integral conditions’. Our fixed point theorems extend the existing results on the problem above.
Highlights
1 Introduction It is well known that the Schauder fixed point theorem plays an important role in nonlinear analysis
In, Darbo [ ] proved a fixed point property for α-set contraction on a closed, bounded and convex subset of Banach spaces in terms of the measure of noncompactness, which was first defined by Kuratowski [ ]
Darbo’s fixed point theorem is a significant extension of the Schauder fixed point theorem, and it plays a key role in nonlinear analysis especially in proving the existence of solutions for a lot of classes of nonlinear equations
Summary
It is well known that the Schauder fixed point theorem plays an important role in nonlinear analysis. In , Darbo [ ] proved a fixed point property for α-set contraction on a closed, bounded and convex subset of Banach spaces in terms of the measure of noncompactness, which was first defined by Kuratowski [ ]. Some generalizations of Darbo’s fixed point theorem have appeared.
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