D-iterative method for solving a delay differential equation and a two-point second-order boundary value problems in Banach spaces. (English) Zbl 1505.47074
Summary: The purpose of this paper is to re-establish the convergence, stability and data dependence results established by [A. Hussain et al., J. Funct. Spaces 2021, Article ID 6675979, 9 p. (2021; Zbl 1505.47110)] and [A. Hussain et al., “Stability data dependency and errors estimation for a general iteration method”, Alexandria Eng. J. 60, No. 1, 703–710 (2021; doi:10.1016/j.aej.2020.10.002)] by removing the strong assumptions imposed on the sequences which were used to obtain their results. In addition, we introduce a modified approach using the D-iterative method to solve a two-point second-order boundary value problem, and also obtain the solution of a delay differential equations using the obtained results in this paper. The results presented in this paper do not only extend and improve the results obtained in [loc. cit.], but further extend and improve some existing results in the literature.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47N20 | Applications of operator theory to differential and integral equations |
Citations:
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