276 research outputs found
A two-parameter control for contractive-like multivalued mappings
We propose a general approach to defining a contractive-like multivalued
mappings which avoids any use of the Hausdorff distance between the sets
and . Various fixed point theorems are proved under a
two-parameter control of the distance function between
a point and the value F(x) \ss X. Here, both parameters are
numerical functions. The first one \a\,:[0,+\i)\rightarrow [1,+\i) controls
the distance between and some appropriate point in comparison
with , whereas the second one \b\,:[0,+\i)\rightarrow [0,1)
estimates with respect to . It appears that the well
harmonized relations between \a and \b are sufficient for the existence of
fixed points of . Our results generalize several known fixed-point theorems
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