Generalized c -almost periodic type functions in ℝ n

M. Kostić

Archivum Mathematicum (2021)

  • Volume: 057, Issue: 4, page 221-253
  • ISSN: 0044-8753

Abstract

top
In this paper, we analyze multi-dimensional quasi-asymptotically c -almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl c -almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically c -almost periodic functions and reconsider the notion of semi- c -periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide certain applications of our results to the abstract Volterra integro-differential equations in Banach spaces.

How to cite

top

Kostić, M.. "Generalized $c$-almost periodic type functions in ${\mathbb {R}}^{n}$." Archivum Mathematicum 057.4 (2021): 221-253. <http://eudml.org/doc/297940>.

@article{Kostić2021,
abstract = {In this paper, we analyze multi-dimensional quasi-asymptotically $c$-almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl $c$-almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically $c$-almost periodic functions and reconsider the notion of semi-$c$-periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide certain applications of our results to the abstract Volterra integro-differential equations in Banach spaces.},
author = {Kostić, M.},
journal = {Archivum Mathematicum},
keywords = {quasi-asymptotically $c$-almost periodic type functions; $(S,\{\mathbb \{D\}\})$-asymptotically $(\omega ,c)$-periodic type functions; $S$-asymptotically $(\omega _\{j\},c_\{j\},\{\mathbb \{D\}\}_\{j\})_\{j\in \{\mathbb \{N\}\}_\{n\}\}$-periodic type functions; semi-$(c_\{j\})_\{j\in \{\mathbb \{N\}\}_\{n\}\}$-periodic type functions; Weyl $c$-almost periodic type functions; abstract Volterra integro-differential equations},
language = {eng},
number = {4},
pages = {221-253},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Generalized $c$-almost periodic type functions in $\{\mathbb \{R\}\}^\{n\}$},
url = {http://eudml.org/doc/297940},
volume = {057},
year = {2021},
}

TY - JOUR
AU - Kostić, M.
TI - Generalized $c$-almost periodic type functions in ${\mathbb {R}}^{n}$
JO - Archivum Mathematicum
PY - 2021
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 057
IS - 4
SP - 221
EP - 253
AB - In this paper, we analyze multi-dimensional quasi-asymptotically $c$-almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl $c$-almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically $c$-almost periodic functions and reconsider the notion of semi-$c$-periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide certain applications of our results to the abstract Volterra integro-differential equations in Banach spaces.
LA - eng
KW - quasi-asymptotically $c$-almost periodic type functions; $(S,{\mathbb {D}})$-asymptotically $(\omega ,c)$-periodic type functions; $S$-asymptotically $(\omega _{j},c_{j},{\mathbb {D}}_{j})_{j\in {\mathbb {N}}_{n}}$-periodic type functions; semi-$(c_{j})_{j\in {\mathbb {N}}_{n}}$-periodic type functions; Weyl $c$-almost periodic type functions; abstract Volterra integro-differential equations
UR - http://eudml.org/doc/297940
ER -

References

top
  1. Alvarez, E., Castillo, S., Pinto, M., ( ω , c ) -Pseudo periodic functions, first order Cauchy problem and Lasota-Wazewska model with ergodic and unbounded oscillating production of red cells, Bound. Value Probl. 106 (2019), 1–20. (2019) MR3974664
  2. Alvarez, E., Castillo, S., Pinto, M., 10.1002/mma.5880, Math. Methods Appl. Sci. 43 (2020), 305–319. (2020) MR4044240DOI10.1002/mma.5880
  3. Alvarez, E., Gómez, A., Pinto, M., 10.14232/ejqtde.2018.1.16, Electron. J. Qual. Theory Differ. Equ. 16 (2018), 1–8. (2018) MR3789407DOI10.14232/ejqtde.2018.1.16
  4. Andres, J., Pennequin, D., 10.1186/1687-2770-2012-141, Bound. Value Probl. 141 (2012), 1–16, doi.org/10.1186/1687-2770-2012-141. (2012) MR3016042DOI10.1186/1687-2770-2012-141
  5. Arendt, W., Batty, C.J.K., Hieber, M., Neubrander, F., Vector-valued Laplace Transforms and Cauchy Problems, Birkhäuser/Springer Basel AG, Basel, 2001. (2001) MR2798103
  6. Besicovitch, A.S., Almost Periodic Functions, Dover Publ., New York, 1954. (1954) 
  7. Blot, J., Cieutat, P., N’Guérékata, G.M., S -asymptotically ω -periodic functions and applications to evolution equations, Afr. Diaspora J. Math. 12 (2011), 113–121. (2011) MR2847308
  8. Chang, Y.-K., Wei, Y., S -asymptotically Bloch type periodic solutions to some semi-linear evolution equations in Banach spaces, Acta Mathematica Sci. 41B (2021), 413–425. (2021) MR4206851
  9. Chaouchi, B., Kostić, M., Pilipović, S., Velinov, D., Semi-Bloch periodic functions, semi-anti-periodic functions and applications, Chelj. Phy. Math. J. 5 (2020), 243–255. (2020) MR4137431
  10. Chávez, A., Khalil, K., Kostić, M., Pinto, M., Multi-dimensional almost automorphic type functions and applications, preprint. 2021. arXiv:2103.10467. 
  11. Chávez, A., Khalil, K., Kostić, M., Pinto, M., Multi-dimensional almost periodic type functions and applications, preprint. 2020. arXiv:2012.00543. 
  12. Chávez, A., Khalil, K., Kostić, M., Pinto, M., Stepanov multi-dimensional almost periodic functions and applications, preprint. 2020. hal-03035195. 
  13. Cheban, D.N., Asymptotically Almost Periodic Solutions of Differential Equations, Hindawi Publishing Corporation, 2009. (2009) MR2603600
  14. Cuevas, C., de Souza, J.C., 10.1016/j.na.2009.09.007, Nonlinear Anal. 72 (2010), 1683–1689. (2010) MR2577568DOI10.1016/j.na.2009.09.007
  15. Diagana, T., Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, Springer-Verlag, New York, 2013. (2013) MR3098423
  16. Diagana, T., Kostić, M., 10.2298/FIL2005629D, Filomat 34 (2020), 1629–1644. (2020) MR4207701DOI10.2298/FIL2005629D
  17. Diagana, T., Kostić, M., Recent Studies in Differential Equations, ch. Chapter 1. Generalized almost automorphic and generalized asymptotically almost automorphic type functions in Lebesgue spaces with variable exponents , pp. 1–28, Nova Science Publishers, New York, 2020. (2020) MR3098423
  18. Diening, L., Harjulehto, P., Hästüso, P., Růužicka, M., 10.1007/978-3-642-18363-8_3, Lecture Notes in Math., Springer, Heidelberg, 2011. (2011) MR2790542DOI10.1007/978-3-642-18363-8_3
  19. Dimbour, W., Manou-Abi, S.M., 10.1007/s00009-018-1071-61660-5446/18/010001-18, Mediterranean J. Math. 15:25 (2018), 18 pp., https://doi.org/10.1007/s00009-018-1071-61660-5446/18/010001-18. (2018) MR3750300DOI10.1007/s00009-018-1071-61660-5446/18/010001-18
  20. Fan, X.L., Zhao, D., On the spaces L p ( x ) ( O ) and W m , p ( x ) ( O ) , J. Math. Anal. Appl. 263 (2001), 424–446. (2001) MR1866056
  21. Fečkan, M., Liu, K., Wang, J.-R., 10.3934/eect.2021006, Evol. Equ. Control Theory, doi:10.3934/eect.2021006. DOI10.3934/eect.2021006
  22. Fedorov, V., Kostić, M., Multi-dimensional Weyl almost periodic type functions and applications, preprint. arXiv:2101.11754. 
  23. Fink, A.M., Almost Periodic Differential Equations, Springer-Verlag, Berlin, 1974. (1974) Zbl0325.34039
  24. Henríquez, H.R., 10.1016/j.na.2012.10.010, Nonlinear Anal. 80 (2013), 135–149. (2013) MR3010761DOI10.1016/j.na.2012.10.010
  25. Henríquez, H.R., Pierri, M., Táboas, P., 10.1016/j.jmaa.2008.02.023, -asymptotically -periodic functions on Banach spaces and applications, J. Math. Appl. Anal. 343 (2008), 1119–1130. (2008) MR2417129DOI10.1016/j.jmaa.2008.02.023
  26. Khalladi, M.T., Kostić, M., Pinto, M., Rahmani, A., Velinov, D., Generalized c -almost periodic functions and applications, Bull. Int. Math. Virtual Inst. 11 (2021), 283–293. (2021) MR4187070
  27. Khalladi, M.T., Kostić, M., Pinto, M., Rahmani, A., Velinov, D., 10.1155/2021/6620625, J. Math. (2021), 5 pp., Article ID 6620625, https://doi.org/10.1155/2021/6620625. (2021) MR4210792DOI10.1155/2021/6620625
  28. Khalladi, M.T., Kostić, M., Rahmani, A., Pinto, M., Velinov, D., 10.1515/msds-2020-0111, Nonauton. Dyn. Syst. 7 (2020), 176–193. (2020) MR4185794DOI10.1515/msds-2020-0111
  29. Kostić, M., Multi-dimensional c -almost periodic type functions and applications, preprint. aXiv:2012.15735. 
  30. Kostić, M., 10.1007/s00574-020-00197-7, Bull. Braz. Math. Soc. (N.S.) 52, 183–212. DOI10.1007/s00574-020-00197-7
  31. Kostić, M., Selected Topics in Almost Periodicity, Book Manuscript, 2021. 
  32. Kostić, M., Weyl almost automorphic functions and applications, preprint 2021. hal-03168920. 
  33. Kostić, M., Almost Periodic and Almost Automorphic Type Solutions to Integro-Differential Equations, W. de Gruyter, Berlin, 2019. (2019) MR3931753
  34. Kostić, M., 10.1016/j.jmaa.2021.124961, J. Math. Anal. Appl. 498 (2021), 32 pp. (2021) MR4202196DOI10.1016/j.jmaa.2021.124961
  35. Kostić, M., 10.1515/msds-2020-0130, Nonauton. Dyn. Syst. 8 (2021), 136–151. (2021) MR4252727DOI10.1515/msds-2020-0130
  36. Kostić, M., Du, W.-S., 10.3390/math8060928, Fixed Point Theory and Dynamical Systems with Applications, 2020, Special issue of Mathematics, Mathematics 8 928; doi:10.3390/math8060928. (2020) MR4202196DOI10.3390/math8060928
  37. Kostić, M., Du, W.-S., 10.3390/math8071052, Fixed Point Theory and Dynamical Systems with Applications, Special issue of Mathematics, 2020, Mathematics 8(7), 1052; https://doi.org/10.3390/math8071052. (2020) MR4202196DOI10.3390/math8071052
  38. Kostić, M., Kumar, V., Pinto, M., Stepanov multi-dimensional almost automorphic type functions and applications, preprint 2021. hal-03227094. 
  39. Kovanko, A.S., Sur la compacié des sysémes de fonctions presque-périodiques généralisées de H. Weyl, C.R. (Doklady) Ac. Sc. URSS 43 (1944), 275–276. (1944) 
  40. Levitan, M., Almost Periodic Functions, G.I.T.T.L., Moscow, 1953, (in Russian). (1953) 
  41. N’Guérékata, G.M., Almost Automorphic and Almost Periodic Functions in Abstract Spaces, Kluwer Acad. Publ., Dordrecht, 2001. (2001) MR1880351
  42. Nguyen, P.Q.H., On variable Lebesgue space, Ph.D. thesis, Kansas State University. Pro- Quest LLC, Ann Arbor, MI, 2011, 63 pp,. (2011) MR2941891
  43. Oueama-Guengai, E.R., N’Guérékata, G.M., 10.1002/mma.5062, Math. Methods Appl. Sci. 41 (2018), 9116–9122. (2018) MR3897769DOI10.1002/mma.5062
  44. Pankov, A.A., Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations, Kluwer Acad. Publ., Dordrecht, 1990. (1990) 
  45. Xie, R., Zhang, C., 10.1155/2015/953540, J. Function Spaces 2015 (2015), 10 pp., Article ID 953540, http://dx.doi.org/10.1155/2015/953540. (2015) MR3326682DOI10.1155/2015/953540
  46. Zaidman, S., Almost-Periodic Functions in Abstract Spaces, Pitman Research Notes in Math., vol. 126, Pitman, Boston, 1985. (1985) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.