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