Korean J. Math. Vol. 30 No. 3 (2022) pp.491-502
DOI: https://doi.org/10.11568/kjm.2022.30.3.491

On Stepanov weighted pseudo almost automorphic solutions of neural networks

Main Article Content

Hyun Mork Lee


In this paper, we investigate some sufficient conditions to guarantee the existence and uniqueness of Stepanov-like weighted pseudo almost periodic solutions of cellular neural networks on Clifford algebra for non-automomous cellular neural networks with multi-proportional delays. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

Article Details


[1] S. Abbas, V.Kavitha and R.Murugesu, Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations, Proc. Indian Acad. Sci. 125 (2015), 323–351. Google Scholar

[2] C. Aouiti, F. Dridi, Q. Hui and E. Moulay, (μ, ν)-pseudo almost automorphic solutions of neutral type Clifford-valued high-order Hopfield neural networks with D operator, Neurocomputing. 53 (2021), 799–828. Google Scholar

[3] C. Aouiti, M. M’hamdi and F. Cherif, The existence and the stability of weighted pseudo almost periodic solution of high-order Hopfield neural network, Springer International Publishing Switzerland. (2016), 478–485. Google Scholar

[4] C. Aouiti, M. M’hamdi and A.Touati, Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays, Neural Process Lett. 45 (2017), 121– 140. Google Scholar

[5] F. Cherif, M. Abdelaziz, Steaponov-like pseudo almost periodic solutions of quaternion-valued for fuzzy recurrent neural networks with mixed delays, Neural Process Lett. 51 (2020), 2211–2243. Google Scholar

[6] T. Diagana, Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, Springer International Publishing Switzerland. 2013. Google Scholar

[7] A.M. Fink, Almost periodic differential equations, Lecture notes in mathematics, Springer Berlin, 377 (1974). Google Scholar

[8] N. Hou, B. Li and Y. Li, Anti-periodic solutions for Clifford-valued high-order Hopfield neural networks with state-dependent and leakage delays, Int.J.Appl.Math.Comput.Sci. 30 (2020), 83–98. Google Scholar

[9] A. N. Kolmogorov, On the representation of continuous functions of many variables by supetposition of continuous functions one variable andaddition, Doklady Akademmi Nauk SSSE, 114 (1957), 953–956. Google Scholar

[10] H. M. Lee, Stepanov almost periodic solutions of Clifford-valued neural works , J. Chungcheong Math. Soc. 35 (2022) no.1, 39–52. Google Scholar

[11] J. Liang, J. Zhang and T. Xiao, Composition of pseudo almost automorphic and asymptotically almost automorphic functions, Journal of Mathematical Analysis and Applications, 340 (2008), 1493–1499. Google Scholar

[12] B. Liu, Global exponential convergence of non-autonomous cellular neural networks with multi- proportional delays, Neurocomputing. 191 (2016), 352–355. Google Scholar

[13] B. Li, Y. Li, Existence and Global Exponential Stability of Pseudo Almost Periodic Solution for Clifford- Valued Neutral High-Order Hopfield Neural Networks With Leakage Delays, IEEE. 7 (2019), 121–140. Google Scholar

[14] M. Maqbul, Stepanov-almost periodic solutions of non-autonomous neutral functional differential equations with functional delay, Mediterr. J. Math. 179 (2018), no.15. Google Scholar

[15] S. Shen, Y. Li, Sp-Almost periodic solutions of Clifford-valued fuzzy cellular neural networks with time-varing delays, Neural Processing Lett. 51 (2020), 1749–1769. Google Scholar