Abstract
The purpose of this paper is to prove strong convergence andT-stability results of some modified hybrid Kirk-Multistep iterations for contractive-type operator in normed linear spaces. Our results show through analytical and numerical approach that the modified hybrid schemes are better in terms of convergence rate than other hybrid Kirk-Multistep iterative schemes in the literature.
Highlights
Numerous papers have been published on the strong convergence and T-stability of various iterative approximations of fixed points for contractive-type operators
Picard iteration (1) which obeys (2) is said to have a fixed point in FT, where FT is the set of all fixed points
The Picard iteration will no longer converge to a fixed point of the operator if contractive condition (2) is weaker
Summary
Numerous papers have been published on the strong convergence and T-stability of various iterative approximations of fixed points for contractive-type operators. The Picard iterative scheme defined for x0 ∈ X xn = Txn−1, n ≥ 1, (1). Was the first iteration to be proved by Banach [10] for a selfmap T in a complete metric space (X, d) satisfying d (Tx, Ty) ≤ cd (x, y) (2). Picard iteration (1) which obeys (2) is said to have a fixed point in FT, where FT is the set of all fixed points. The Picard iteration will no longer converge to a fixed point of the operator if contractive condition (2) is weaker. There is a need to consider other iterative procedures
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