Skip to content
BY 4.0 license Open Access Published by De Gruyter Open Access December 4, 2020

c-Almost periodic type functions and applications

  • M. T. Khalladi , M. Kostić , M. Pinto , A. Rahmani and D. Velinov

Abstract

In this paper, we introduce several various classes of c-almost periodic type functions and their Stepanov generalizations, where c ∈ ℂ and |c| = 1. We also consider the corresponding classes of c-almost periodic type functions depending on two variables and prove several related composition principles. Plenty of illustrative examples and applications are presented.

MSC 2010: 42A75; 43A60; 47D99

References

[1] E. Alvarez, A. Gómez and M. Pinto, (ω, c)-Periodic functions and mild solution to abstract fractional integro-differential equations, Electron. J. Qual. Theory Differ. Equ, 16 (2018), 1–8.10.14232/ejqtde.2018.1.16Search in Google Scholar

[2] E. Alvarez, S. Castillo and M. Pinto, (ω, c)-Pseudo periodic functioins, first order Cauchy problem and Lasota-Wazewska model with ergodic and unbounded oscillating production of red cells, Bound. Value Probl, 106 (2019), 1–20.Search in Google Scholar

[3] E. Alvarez, S. Castillo and M. Pinto, (ω, c)-Asymptotically periodic functions, first-order Cauchy problem, and Lasota-Wazewska model with unbounded oscillating production of red cells, Math. Methods Appl. Sci, 43 (2020), 305–319.10.1002/mma.5880Search in Google Scholar

[4] J. Andres and D. Pennequin, Semi-periodic solutions of difference and differential equations, Bound. Value Probl, 141 (2012), 1–16.Search in Google Scholar

[5] H. Bart and S. Goldberg, Characterizations of almost periodic strongly continuous groups and semigroups, Math. Ann, 236 (1978), 105–116.10.1007/BF01351384Search in Google Scholar

[6] A. S. Besicovitch, Almost Periodic Functions, Dover Publ, New York, 1954.Search in Google Scholar

[7] P.H. Bezandry and T. Diagana, Almost Periodic Stochastic Processes, Springer, New York, 2011.10.1007/978-1-4419-9476-9Search in Google Scholar

[8] C. Blatter, Dense set in the unit circle, https://math.stackexchange.com/questions/1569152/dense-set-in-the-unit-circle-reference-needed.Search in Google Scholar

[9] H. Bohr, Zur theorie der fastperiodischen Funktionen I; II; III. Acta Math, 45 (1924), 29–127; H6 (1925), 101–214; HT (1926), 237–281.10.1007/BF02395468Search in Google Scholar

[10] B. Chaouchi, M. Kostić, S. Pilipović and D. Velinov, Semi-Bloch periodic functions, semi-anti-periodic functions and applications, Chelj. Phy. Math. J, 5 (2020), 243–255.Search in Google Scholar

[11] C. Corduneanu, Almost Periodic Functions, Wiley, New York, 1968.Search in Google Scholar

[12] C. Corduneanu, Almost Periodic Oscillations and Waves, Springer-Verlag, Berlin, 2010.10.1007/978-0-387-09819-7Search in Google Scholar

[13] J. de Vries, Elements of Topological Dynamics, Mathematics and its applications, vol. 257, Springer-Science+Business Media, B.V., Dordrecht, 1993.10.1007/978-94-015-8171-4Search in Google Scholar

[14] T. Diagana, Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, Springer-Verlag, New York, 2013.10.1007/978-3-319-00849-3Search in Google Scholar

[15] A.M. Fink, Almost Periodic Differential Equations, Springer-Verlag, Berlin, 1974.10.1007/BFb0070324Search in Google Scholar

[16] G.M.N’Guérékata, Almost Automorphic and Almost Periodic Functions in Abstract Spaces, Kluwer Acad. Publ, Dordrecht, 2001.10.1007/978-1-4757-4482-8Search in Google Scholar

[17] A. Haraux and P. Souplet, An example of uniformly recurrent function which is not almost periodic, J. Fourier Anal. Appl, 10 (2004), 217–220.10.1007/s00041-004-8012-4Search in Google Scholar

[18] W. Long and H.-S. Ding, 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:10.1155/2011/654695.10.1155/2011/654695Search in Google Scholar

[19] M.T. Khaladdi, M. Kostić, A. Rahmani and D. Velinov, (ω, c)-Almost periodic type functions and applications, Filomat, submitted.Search in Google Scholar

[20] M.T. Khalladi, M. Kostić, A. Rahmani and D. Velinov, (ω, c)- Pseudo almost periodic functions, (ω, c)- pseudo almost auto-morphic functions and applications, Facta Univ. Ser. Math. Inform, in press.Search in Google Scholar

[21] M.T. Khalladi, M. Kostić, M. Pinto, A. Rahmani and D. Velinov, Semi-c-periodic functions and applications, preprint.Search in Google Scholar

[22] M. Kostić, Almost Periodic and Almost Automorphic Type Solutions to Integro-Differential Equations, W. de Gruyter, Berlin, 2019.10.1515/9783110641851Search in Google Scholar

[23] M. Kostić, Almost periodic type functions and densities, Evol. Equ. Control Theory, submitted. https://hal.archives-ouvertes.fr/hal-02523952.Search in Google Scholar

[24] M. Kostić, Composition principles for almost periodic type functions and applications, J. Fract. Calc. Appl, submitted.Search in Google Scholar

[25] M. Kostić and D. Velinov, A note on almost anti-periodic functions in Banach spaces, Kragujevac J. Math. 44 (2020), 287–297.10.46793/KgJMat2002.287KSearch in Google Scholar

[26] G. Mophou, G. M. N’ Guérékata, An existence result of (ω,c)-periodic mild solutions to some fractional differential equation, Nonlinear Studies 27 (2020), 167–175.Search in Google Scholar

[27] M. Pinto, Ergodicity and oscillations, Conference in Universidad Católica del Norte, Antofagasta, Chile, 2014.Search in Google Scholar

[28] S. Zaidman, Almost-Periodic Functions in Abstract Spaces, Pitman Research Notes in Math, Vol. 126, Pitman, Boston, 1985.Search in Google Scholar

Received: 2020-05-18
Accepted: 2020-11-09
Published Online: 2020-12-04
Published in Print: 2020-01-01

© 2018 M. T. Khalladi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Downloaded on 26.4.2024 from https://www.degruyter.com/document/doi/10.1515/msds-2020-0111/html
Scroll to top button