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Order Theoretic Common n-tuple Fixed Point
Authors: Yaé Ulrich Gaba
Number of views: 453
In this article, we solve an open problem initially suggested in [2], namely:
Let (X,d) be a Hausdorff left K-complete T0-quasi-pseudometric space, φ : X → R be a bounded
from above function and the preorder induced by φ. Let F : X × X → X and Gi : X →
X;i = 1, 2, · · · , N for N > 2 be N + 1 d-sequentially continuous mapping on X such that the pairs
{F; Gi};i = 1, 2, · · · , N are weakly left-related.
Problem:
1. Can we prove that F, G1, · · · , GN have a common coupled fixed point in X?
2. Alternatively, what could be a correct formulation of the statement, using the induced preorder
and the weakly left-related property that guarantees a positive answer?
We answer this question by the affirmative. In fact we prove that a more general result holds when
F : X
n → X for a natural number n > 2.