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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.

Asymptotically almost automorphic solutions of differential equations with piecewise constant argument

Hui-Sheng Ding, Shun-Mei Wan (2017)

Open Mathematics

This paper is concerned with the existence and uniqueness of asymptotically almost automorphic solutions to differential equations with piecewise constant argument. To study that, we first introduce several notions about asymptotically almost automorphic type functions and obtain some properties of such functions. Then, on the basis of a systematic study on the associated difference system, the existence and uniqueness theorem is established. Compared with some earlier results, we do not assume...

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