Successive Approximation of Implicit Multistep Type Iterative Algorithms in Locally Convex Spaces

Eke, Kanayo Stella and Akewe, Hudson (2019) Successive Approximation of Implicit Multistep Type Iterative Algorithms in Locally Convex Spaces. Asian Journal of Scientific Research, 12 (3). pp. 361-368.

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Abstract

Background and Objectives: The application of implicit fixed point iterative algorithms have been greatly employed in many physical systems as the implicit algorithms provide better approximation than their corresponding explicit algorithms and are very efficient in reducing the computational cost of the fixed point problems. The objectives of this study, therefore; were in three folds: (1) To develop implicit hybrid Jungck-Kirk multistep iterative algorithms in a metrizable locally convex space, (2) Prove its convergence to the unique common fixed point of a pair of weakly compatible generalized contractive-type operators (S, T) and (3) Demonstrate the application of the convergence results with some examples. Materials and Methods: Analytical method was used to prove the main theorem, while numerical method was to demonstrate the application of the convergence result. Results: Strong convergence analytical and numerical results constitute the main results of this work. Conclusion: The results obtained from this study showed that the implicit hybrid Jungck- Kirk multistep iterative algorithms have good potentials for further applications, especially in relation to rate of convergence.

Item Type:	Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User:	Mrs Patricia Nwokealisi
Date Deposited:	13 Aug 2019 07:18
Last Modified:	13 Aug 2019 07:18
URI:	http://eprints.covenantuniversity.edu.ng/id/eprint/12831

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