Abstract
In this note we prove that a kind of mappings depending on k arguments introduced in (Paknazar et al. in Fixed Point Theory Appl. 2013:111, 2013) only depend on their first argument. Therefore, results in that paper reduce to the unidimensional case. We also include some commentaries about the different notions of multidimensional fixed point.MSC:46T99, 47H10, 47H09, 54H25.
Highlights
In this note we prove that a kind of mappings depending on k arguments introduced in (Paknazar et al in Fixed Point Theory Appl. 2013:111, 2013) only depend on their first argument
Notice that if F verifies the new g-monotone property, we have showed that there exists a mapping f : X → X such that
Do not let us to show the existence of fixed points using the classical mixed monotone property
Summary
In this note we prove that a kind of mappings depending on k arguments introduced in (Paknazar et al in Fixed Point Theory Appl. 2013:111, 2013) only depend on their first argument. Paknazar et al [ ] introduced the concept of new g-monotone property for a mapping F : Xk → X as follows. Theorem Let (X, ) be a partially ordered set, and let g : X → X and F : Xk → X (k ≥ ) be two given mappings such that F has the new g-monotone property.
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