Abstract
In this work, we give a new definition of G-monotone pointwise contraction mappings in metric spaces endowed with a graph. Then we obtain sufficient conditions for the existence of a fixed point for such mappings. The proofs are based on the crucial inequality (GK).
Highlights
The notion of asymptotic pointwise mappings was introduced in [ – ]
Recently a new direction has been discovered dealing with the extension of the Banach contraction principle to metric spaces endowed with a partial order
For more examples on fixed points of multivalued mappings on metric spaces endowed with a graph, see [ ]
Summary
The notion of asymptotic pointwise mappings was introduced in [ – ]. The author [ ] showed the existence of fixed points for monotone multivalued mappings on a metric space with a graph. We investigate the fixed point theory of pointwise G-monotone contraction mappings.
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