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Asymptotic fuzzy contractive mappings in fuzzy metric spaces

Dhananjay Gopal, Juan Martínez-Moreno, Rosana Rodríguez-López (2024)

Kybernetika

Fixed point theory in fuzzy metric spaces has grown to become an intensive field of research. However, due to the complexity involved in the nature of fuzzy metrics, the authors need to develop innovative machinery to establish new fixed point theorems in such kind of spaces. In this paper, we propose the concepts of asymptotic fuzzy ψ -contractive and asymptotic fuzzy Meir-Keeler mappings, and describe some new machinery by which the corresponding fixed point theorems are proved. In this sense,...

Asymptotic stability in the Schauder fixed point theorem

Mau-Hsiang Shih, Jinn-Wen Wu (1998)

Studia Mathematica

This note presents a theorem which gives an answer to a conjecture which appears in the book Matrix Norms and Their Applications by Belitskiĭ and Lyubich and concerns the global asymptotic stability in the Schauder fixed point theorem. This is followed by a theorem which states a necessary and sufficient condition for the iterates of a holomorphic function with a fixed point to converge pointwise to this point.

Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains

Simeon Reich, David Shoikhet (1998)

Studia Mathematica

Let D be a hyperbolic convex domain in a complex Banach space. Let the mapping F ∈ Hol(D,D) be bounded on each subset strictly inside D, and have a nonempty fixed point set ℱ in D. We consider several methods for constructing retractions onto ℱ under local assumptions of ergodic type. Furthermore, we study the asymptotic behavior of the Cesàro averages of one-parameter semigroups generated by holomorphic mappings.

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