Remotely c -almost periodic type functions in ℝ n

Marco Kostić; Vipin Kumar

Archivum Mathematicum (2022)

  • Volume: 058, Issue: 2, page 85-104
  • ISSN: 0044-8753

Abstract

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In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely c -almost periodic functions in ℝ n , slowly oscillating functions in ℝ n , and further analyze the recently introduced class of quasi-asymptotically c -almost periodic functions in ℝ n . We provide certain applications of our theoretical results to the abstract Volterra integro-differential equations and the ordinary differential equations.

How to cite

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Kostić, Marco, and Kumar, Vipin. "Remotely $c$-almost periodic type functions in ${\mathbb {R}}^{n}$." Archivum Mathematicum 058.2 (2022): 85-104. <http://eudml.org/doc/298323>.

@article{Kostić2022,
abstract = {In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely $c$-almost periodic functions in $\{\mathbb \{R\}\}^\{n\},$ slowly oscillating functions in $\{\mathbb \{R\}\}^\{n\},$ and further analyze the recently introduced class of quasi-asymptotically $c$-almost periodic functions in $\{\mathbb \{R\}\}^\{n\}.$ We provide certain applications of our theoretical results to the abstract Volterra integro-differential equations and the ordinary differential equations.},
author = {Kostić, Marco, Kumar, Vipin},
journal = {Archivum Mathematicum},
keywords = {remotely $c$-almost periodic functions in $\{\mathbb \{R\}\}^\{n\}$; slowly oscillating functions in $\{\mathbb \{R\}\}^\{n\}$; quasi-asymptotically $c$-almost periodic functions in $\{\mathbb \{R\}\}^\{n\}$; abstract Volterra integro-differential equations; Richard-Chapman ordinary differential equation with external perturbation},
language = {eng},
number = {2},
pages = {85-104},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Remotely $c$-almost periodic type functions in $\{\mathbb \{R\}\}^\{n\}$},
url = {http://eudml.org/doc/298323},
volume = {058},
year = {2022},
}

TY - JOUR
AU - Kostić, Marco
AU - Kumar, Vipin
TI - Remotely $c$-almost periodic type functions in ${\mathbb {R}}^{n}$
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 2
SP - 85
EP - 104
AB - In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely $c$-almost periodic functions in ${\mathbb {R}}^{n},$ slowly oscillating functions in ${\mathbb {R}}^{n},$ and further analyze the recently introduced class of quasi-asymptotically $c$-almost periodic functions in ${\mathbb {R}}^{n}.$ We provide certain applications of our theoretical results to the abstract Volterra integro-differential equations and the ordinary differential equations.
LA - eng
KW - remotely $c$-almost periodic functions in ${\mathbb {R}}^{n}$; slowly oscillating functions in ${\mathbb {R}}^{n}$; quasi-asymptotically $c$-almost periodic functions in ${\mathbb {R}}^{n}$; abstract Volterra integro-differential equations; Richard-Chapman ordinary differential equation with external perturbation
UR - http://eudml.org/doc/298323
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. Arendt, W., Batty, C.J.K., Hieber, M., Neubrander, F., Vector-valued Laplace transforms and Cauchy problems, Birkhäuser, Springer Basel AG, 2001. (2001) MR2798103
  5. Besicovitch, A.S., Almost Periodic Functions, Dover Publ., New York, 1954. (1954) MR0068029
  6. Blot, J., Cieutat, P., N’Guérékata, G.M., S-asymptotically ω -periodic functions and applications to evolution equations, -asymptotically -periodic functions and applications to evolution equations, African Diaspora J. Math. 12 (2011), 113–121. (2011) MR2847308
  7. Brindle, D., S -asymptotically ω -periodic functions and sequences and applications to evolution equations, Ph.D. thesis, Morgan State University, 2019, https://mdsoar.org/handle/11603/17680. (2019) MR4071576
  8. Chang, Y.-K., Wei, Y., 10.1007/s10473-021-0206-1, Acta Math. Sci. 41B (2021), 413–425. (2021) MR4206851DOI10.1007/s10473-021-0206-1
  9. Chávez, A., Khalil, K., Kostić, M., Pinto, M., Multi-dimensional almost periodic type functions and applications, submitted 2020, arXiv:2012.00543. 
  10. Chávez, A., Khalil, K., Kostić, M., Pinto, M., 10.1007/s00574-022-00284-x, Bull. Braz. Math. Soc. (N.S.) (2022), 1–51, https/doi.org/10.1007/s00574-022-00284-x. (2022) MR4458789DOI10.1007/s00574-022-00284-x
  11. 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
  12. Diagana, T., Almost automorphic type and almost periodic type functions in abstract spaces, Springer-Verlag, New York, 2013. (2013) MR3098423
  13. Dimbour, W., Manou-Ab, S.M., 10.1007/s00009-018-1071-61660-5446/18/010001-18, Mediterranean J. Math. 15 (1) (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
  14. Fink, A.M., Almost periodic differential equations, Springer-Verlag, Berlin, 1974. (1974) MR0460799
  15. Friedman, A., Partial differential equations of parabolic type, Prentice Hall, Englewood Cliffs, NJ, 1964, xiv+347 pp. (1964) MR0181836
  16. Garcia, S.R., Remembering Donald Sarason (1933-2017), Notices Amer. Math. Soc. 65 (2018), 195–200. (2018) MR3751316
  17. Haraux, A., Souplet, P., 10.1007/s00041-004-8012-4, J. Fourier Anal. Appl. 10 (2004), 217–220. (2004) MR2054309DOI10.1007/s00041-004-8012-4
  18. 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
  19. 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
  20. 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
  21. Kostić, M., Multi-dimensional c -almost periodic type functions and applications, Electron. J. Differential Equations, in press, aXiv:2012.15735. MR4252727
  22. Kostić, M., Generalized semigroups and cosine functions, Mathematical Institute SANU, Belgrade, 2011. (2011) MR2790849
  23. Kostić, M., Almost periodic and almost automorphic type solutions to integro-differential equations, W. de Gruyter, Berlin, 2019. (2019) MR3931753
  24. Kostić, M., 10.5817/AM2021-4-221, Arch. Math. (Brno) 57 (2021), 221–253. (2021) MR4346112DOI10.5817/AM2021-4-221
  25. Kostić, M., 10.1515/msds-2020-0130, Nonauton. Dyn. Syst. 8 (2021), 136–151. (2021) MR4252727DOI10.1515/msds-2020-0130
  26. Kostić, M., 10.1007/s00574-020-00197-7, Bull. Braz. Math. Soc. (N.S.) 52 (2021), 183–212. (2021) MR4253402DOI10.1007/s00574-020-00197-7
  27. Kostić, M., 10.3934/eect.2021008, Evol. Equ. Control Theory 11 (2) (2022), 457–486. (2022) MR4376332DOI10.3934/eect.2021008
  28. Kostić, M., Selected topics in almost periodicity, W. de Gruyter, Berlin, 2022. (2022) 
  29. Kovanko, A.S., Sur la compacié des systémes de fonctions presque-périodiques généralisées de H. Wey, C.R. (Doklady) Ac. Sc. URSS 43 (1944), 275–276. (1944) MR0012148
  30. Levitan, M., Almost periodic functions, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1953, 396 pp. (in Russian). (1953) MR0060629
  31. Maulén, C., Castillo, S., Kostić, M., Pinto, M., 10.1155/2021/9985454, J. Math. 2021 (2021), 9 pp., Article ID 9985454, 9 pp., https://doi.org/10.1155/2021/9985454. (2021) MR4265296DOI10.1155/2021/9985454
  32. N’Guérékata, G.M., Almost automorphic and almost periodic functions in abstract spaces, Kluwer Acad. Publ. Dordrecht, 2001. (2001) MR1880351
  33. 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
  34. Pankov, A.A., Bounded and almost periodic solutions of nonlinear operator differential equations, Kluwer Acad. Publ., Dordrecht, 1990. (1990) MR1120781
  35. Rabinovich, V.S., Roch, S., 10.1088/0305-4470/39/26/007, J. Phys. A 39 (2006), 8377–8394. (2006) MR2238507DOI10.1088/0305-4470/39/26/007
  36. Sarason, D., 10.1512/iumj.1977.26.26066, Indiana Univ. Math. J. 26 (1977), 817–838. (1977) MR0463968DOI10.1512/iumj.1977.26.26066
  37. Sarason, D., 10.1090/conm/032/769512, Contemp. Math. 32 (1984), 237–242. (1984) MR0769512DOI10.1090/conm/032/769512
  38. Sarason, D., The Banach algebra of slowly oscillating functions, Houston J. Math. 33 (4) (2007), 1161–1182. (2007) MR2350087
  39. 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
  40. Yang, F., Zhang, C., 10.1155/2010/471491, Bound. Value Probl. 2010 (2010), 12 pp., Article ID 471491, doi:10.1155/2010/471491. (2010) MR2753238DOI10.1155/2010/471491
  41. Yang, F., Zhang, C., 10.11650/twjm/1500406160, Taiwanese J. Math. 15 (2011), 43–57. (2011) MR2780270DOI10.11650/twjm/1500406160
  42. Zaidman, S., Almost-periodic functions in abstract spaces, Pitman Research Notes in Math., vol. 126, Pitman, Boston, 1985. (1985) MR0790316
  43. Zhang, C., Guo, Y., 10.1155/2007/60239, J. Inequal. Appl. 2007 (2007), 9 pp., Article ID 60239, doi:10.1155/2007/60239. (2007) MR2304457DOI10.1155/2007/60239
  44. Zhang, C., Jiang, L., 10.1016/j.na.2005.10.036, Nonlinear Anal. 65 (2006), 1613–1623. (2006) MR2248688DOI10.1016/j.na.2005.10.036
  45. Zhang, C., Jiang, L., 10.1016/j.aml.2007.08.007, Appl. Math. Lett. 21 (2008), 761–768. (2008) MR2436161DOI10.1016/j.aml.2007.08.007
  46. Zhang, S., Piao, D., 10.5402/2011/415358, ISRN Math. Anal. 2011 (2011), 13 pp., Article ID 415358, doi:10.5402/2011/415358. (2011) MR2772323DOI10.5402/2011/415358

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