[FORTHCOMING] Metrical Weyl almost automorphy and applications

In this paper, we reconsider and slightly generalize various classes of Weyl almost automorphic functions ([29], [33]). More precisely, we consider here various classes of metrically Weyl almost automorphic functions of the form $$$F : {\mathbb R}^{n} \times X \rightarrow Y$$$ and metrically Weyl almost automorphic sequences of the form $$$F : {\mathbb Z}^{n} \times X \rightarrow Y$$$, where $$$X$$$ and $$$Y$$$ are complex Banach spaces. The main structural characterizations for the introduced classes of metrically Weyl almost automorphic functions and sequences are established. In addition to the above, we provide several illustrative examples, useful remarks and applications of the theoretical results.

In this paper, we reconsider and slightly generalize various classes of Weyl almost automorphic functions ([29], [33]). More precisely, we consider here various classes of metrically Weyl almost automorphic functions of the form $$$F : {\mathbb R}^{n} \times X \rightarrow Y$$$ and metrically Weyl almost automorphic sequences of the form $$$F : {\mathbb Z}^{n} \times X \rightarrow Y$$$, where $$$X$$$ and $$$Y$$$ are complex Banach spaces. The main structural characterizations for the introduced classes of metrically Weyl almost automorphic functions and sequences are established. In addition to the above, we provide several illustrative examples, useful remarks and applications of the theoretical results.

Metrically Weyl almost automorphic functions metrically Weyl almost automorphic sequences abstract Volterra integro-differential equations abstract Volterra difference equations

Metrically Weyl almost automorphic functions metrically Weyl almost automorphic sequences abstract Volterra integro-differential equations abstract Volterra difference equations