Abstract
AbstractIn a real Banach space X and a complete metric space M, we consider a compact mapping C defined on a closed and bounded subset A of X with values in M and the operator $$T:A\times C(A) \rightarrow X$$
T
:
A
×
C
(
A
)
→
X
. Using a new type of equicontractive condition for a certain family of mappings and $$\beta $$
β
-condensing operators defined by the Hausdorff measure of noncompactness we prove that the operator $$x\mapsto T(x,C(x))$$
x
↦
T
(
x
,
C
(
x
)
)
has a fixed point. The obtained results are applied to the initial value problem.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,Modelling and Simulation
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