International Journal of Nonlinear Analysis and Applications

Approximation results of non-homogeneous Cauchy problem of semigroup of linear operators

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Ilorin, Ilorin, Nigeria

2 Department of Mathematical Sciences, Olusegun Agagu University of Science and Technology, Okitipupa, Nigeria

3 Department of Mathematics, Federal University, Oye-Ekiti, Nigeria

Abstract

In this paper, results of $\omega$-order reversing partial contraction mapping generated by approximation results of non-homogeneous Cauchy problem were presented. We investigated the concepts of $C'$, strong and, respectively, $C^0$-solution. We established that $Z:D(Z)\subseteq X\to X$ is the infinitesimal generator of a $C_0$-semigroup of contraction, $\xi\in X$ and $f\in L^2(a,b;X)$. Furthermore, we deduced that the unique $C^0$-solution is strong and that the class is absolutely continuous on $[a,b]$.\\

Keywords

[1] A.Y. Akinyele, O.E. Jimoh, J.B. Omosowon, and K.A. Bello, Results of semigroup of linear operator generating a continuous time Markov semigroup, Earthline J. Math. Sci. 10 (2022), no. 1, 97–108.
[2] A.Y. Akinyele, K. Rauf, J.B. Omosowon, B. Sambo, and G.O. Ibrahim, Differentiable and analytic results on ω-order preserving partial contraction mapping in semigroup of linear operator, Asian Pacific J. Math. Appl. 8 (2021), no. 2, 1–13.
[3] A.V. Balakrishnan, An operator calculus for infinitesimal generators of semigroup, Trans. Amer. Math. Soc. 91 (1959), 330–353.
[4] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133–181.
[5] H. Brezis and T. Gallouet, Nonlinear Schrödinger evolution equation, Nonlinear Anal. TMA 4 (1980), 677–682.
[6] R. Chill and Y. Tomilov, Stability Operator Semigroup, Banach Center Publication 75, Polish Academy of Sciences, Warsaw, 2007.
[7] E.B. Davies, Linear Operator and their Spectra, Cambridge Studies in Advanced Mathematics, Cambridge University Press, New York, 2007.
[8] K. Engel and R. Nagel, One-parameter Semigroups for Linear Equations, Graduate Texts in Mathematics, 194, Springer, New York, 2000.
[9] J.B. Omosowon, A.Y. Akinyele, O.Y. Saka-Balogun, and M.A. Ganiyu, Analytic results of semigroup of linear operator with dynamic boundary conditions, Asian J. Math. Appl. 2020 (2020), 1–10.
[10] J.B. Omosowon, A.Y. Akinyele, and F.M. Jimoh, Dual properties of ω-order reversing partial contraction mapping in semigroup of linear operator, Asian J. Math. Appl. 2021 (2021), 1–10.
[11] J.B. Omosowon, A.Y. Akinyele, and O.Y. Saka-Balogun, Results of semigroup of linear operator generating a wave equation, Earthline J. Math. Sci. 11 (2023), no. 1, 173–182.
[12] K. Rauf and A.Y. Akinyele, Properties of ω-order-preserving partial contraction mapping and its relation to C₀-semigroup, Int. J. Math. Comput. Sci. 14 (2019), no. 1, 61–68.
[13] K. Rauf, A.Y. Akinyele, M.O. Etuk, R.O. Zubair, and M.A. Aasa, Some result of stability and spectra properties on semigroup of linear operators, Adv. Pure Math. 9 (2019), 43–51.
[14] I.I. Vrabie, C₀-semigroup and Application, Mathematics Studies, 191, Elsevier, North-Holland, 2003.
[15] K. Yosida, On the differentiability and representation of one-parameter semigroups of linear operators, J. Math. Soc. Jap. 1 (1948), 15–21.
International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 10 February 2026
  • Receive Date: 25 March 2024
  • Revise Date: 20 January 2025
  • Accept Date: 30 January 2025