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Suppose that f : X → X is a G-graphic contraction.
Let f : X → X be a G-graphic contraction which is G-orbitally continuous.
We can now give the main result for G-graphic contractions.
Let f : X → X be a G-graphic contraction with the constant a.
A simple case-by-case calculation shows that f is a G-graphic contraction.
Definition 1.2 An operator f : X → X is called a Banach G-graphic contraction if.
Then G is weakly connected, X f is nonempty and f is a G-graphic contraction which fails to be a G-contraction.
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