STEPANOV $\rho$-ALMOST PERIODIC FUNCTIONS IN GENERAL METRIC
Abstract
In this paper, we analyze various classes of multi-dimensional Stepanov $\rho$-almost periodic functions in general metric. The main structural properties for the introduced classes of Stepanov almost periodic type functions are established. We also provide an illustrative application to the abstract degenerate semilinear fractional differential equations.
Keywords
Full Text:
PDFReferences
bibitem{besik}
{sc A. S. Besicovitch:}
textit{Almost Periodic Functions.}
Dover Publ, New York, 1954.
bibitem{bohr-folner}
{sc H. Bohr, E. F$o$lner:}
textit{On some types of functional spaces: A contribution to the theory of almost periodic functions.}
Acta Math. {bf 76} (1944) 31--155.
bibitem{marko-manuel-ap}
{sc A. Ch'avez, K. Khalil, M. Kosti'c, M. Pinto:}
textit{Multi-dimensional almost periodic type functions and applications.}
submitted (2020). arXiv:2012.00543.
bibitem{diagana}
{sc T. Diagana:}
textit{Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces.}
Springer, New York, 2013.
bibitem{variable}
{sc L. Diening, P. Harjulehto, P. H"ast"uso, M. Ruzicka:}
{it Lebesgue and Sobolev Spaces with Variable
Exponents.}
Lecture Notes in Mathematics, 2011. Springer, Heidelberg, 2011.
bibitem{rho}
{sc M. Fev{c}kan, M. T. Khalladi, M. Kosti'{c}, A. Rahmani:}
textit{Multi-dimensional $rho$-almost periodic type functions and applications.}
submitted (2021). arXiv:2109.10223.
bibitem{fink}
{sc A. M. Fink:}
textit{Almost Periodic Differential Equations.}
Springer-Verlag, Berlin, 1974.
bibitem{gaston}
{sc G. M. N'Gu' er' ekata:}
textit{Almost Automorphic and Almost Periodic Functions
in Abstract Spaces.}
Kluwer Acad. Publ., Dordrecht, 2001.
bibitem{nova-mono}
{sc M. Kosti'c:}
textit{Almost Periodic and Almost Automorphic Type Solutions to Integro-Differential Equations.}
W. de Gruyter, Berlin, 2019.
bibitem{nova-selected}
{sc M. Kosti'c:}
textit{Selected Topics in Almost Periodicity.}
W. de Gruyter, Berlin, 2022.
bibitem{nova-almost}
{sc M. Kosti'c:}
textit{Recent Trends in Almost Periodicity.}
Book Manuscript, 2022.
bibitem{brno}
{sc M. Kosti'c:}
textit{Generalized $c$-almost periodic type functions in ${mathbb R}^{n}.$}
Arch. Math. (Brno) {bf 57} (2021), 221--253.
bibitem{ejmaa-2022}
{sc M. Kosti'c:}
textit{Stepanov and Weyl classes of multi-dimensional $rho$-almost periodic type functions.}
Electronic J. Math. Anal. Appl. {bf 10} (2022), 11--35.
bibitem{metrical}
{sc M. Kosti'c:}
textit{Metrical almost periodicity and applications.}
submitted (2021). arXiv:2111.14614.
bibitem{weyl-metric}
{sc M. Kosti'c:}
textit{Weyl $rho$-almost periodic functions in general metric.}
submitted (2021).
bibitem{188}
{sc M. Levitan:}
textit{Almost Periodic Functions.}
G.I.T.T.L., Moscow, 1953 (in Russian).
bibitem{long-ding}
{sc W. Long, H.-S. Ding:}
textit{Composition theorems of Stepanov almost periodic functions
and Stepanov-like pseudo-almost periodic functions.}
Adv. Difference Equ., Vol. 2011, Article ID 654695, 12 pages, doi:10.1155/2011/654695.
bibitem{pankov}
{sc A. A. Pankov:}
textit{Bounded and Almost Periodic Solutions of Nonlinear Operator
Differential Equations.}
Kluwer Acad. Publ., Dordrecht, 1990.
bibitem{30}
{sc S. Zaidman:}
textit{Almost-Periodic Functions in Abstract Spaces.}
Pitman Research Notes in
Math., Vol. textbf{126}, Pitman, Boston,
DOI: https://doi.org/10.22190/FUMI211217024K
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)