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Hence is unique coupled point of coincidence of and.
Then, (fu, fu) is a coupled point of coincidence of f, S, and T. By the uniqueness of coupled point of coincidence, we have fu = fx.
That is, (fu, fu) is a coupled point of coincidence of f, S, and T. By the uniqueness of coupled point of coincidence, we have fu = fx.
Then ( g u, g u ) is a coupled point of coincidence, and also we have ( u, u ) is a coupled point of coincidence.
Then and therefore is unique coupled point of coincidence of and.
Then a coupled point of A is a fixed point of T and vice versa.
First, we will show that the coupled point of coincidence is unique.
Then F and g have a unique coupled point of coincidence.
We shall show that the coupled point of coincidence is unique.
Hence, ( x, y ) is a coupled point of coincidence of F and g.
Therefore, ( g x, g y ) is the unique coupled point of coincidence of F and g.
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