Turkish Journal of Mathematics
Abstract
In this paper, we analyze Levitan and Bebutov metrical approximations of functions $F :\Lambda \times X \rightarrow Y$ by trigonometric polynomials and $\rho$-periodic type functions, where $\emptyset \neq \Lambda \subseteq {\mathbb R}^{n}$, $X$ and $Y$ are complex Banach spaces, and $\rho$ is a general binary relation on $Y$. We also analyze various classes of multidimensional Levitan almost periodic functions in general metric and multidimensional Bebutov uniformly recurrent functions in general metric. We provide several applications of our theoretical results to the abstract Volterra integro-differential equations and the partial differential equations.
DOI
10.55730/1300-0098.3393
Keywords
Levitan metrical almost periodicity, Bebutov metrical almost periodicity, abstract Volterra integro-differential equations
First Page
769
Last Page
793
Recommended Citation
CHAOUCHI, BELKACEM; KOSTIC, MARKO; and VELINOV, DANIEL
(2023)
"Metrical almost periodicity, metrical approximations of functions and applications,"
Turkish Journal of Mathematics: Vol. 47:
No.
2, Article 25.
https://doi.org/10.55730/1300-0098.3393
Available at:
https://journals.tubitak.gov.tr/math/vol47/iss2/25
