58 research outputs found
On Multistep Iterative Scheme for Approximating the Common Fixed Points of Contractive-Like Operators
We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa, and Jungck-Noor iterations can also be used to approximate the common fixed points of such maps. The results are improvements, generalizations, and extensions of the work of Olatinwo and Imoru (2008), Olatinwo (2008). Consequently, several results in literature are generalized
Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators
In this paper, we introduce Kirk-multistep and Kirk-multistep-SP iterative schemes and
prove their strong convergences and stabilities for contractive-type operators in normed linear spaces. By taking numerical examples, we compare the convergence
speed of our schemes (Kirk-multistep-SP iterative schemes) with the others (Kirk-SP,Kirk-Noor, Kirk-Ishikawa, Kirk-Mann and Kirk iterative schemes) for this class of operators. Our results generalize and extend most convergence and stability results in the literature
A Picard-S Iterative Scheme for Approximating Fixed Point of Weak-Contraction Mappings
We study the convergence analysis of a Picard-S iteration method for a
particular class of weak-contraction mappings. Furthermore, we prove a data
dependence result for fixed point of the class of weak-contraction mappings
with the help of the Picard-S iteration methods
THE EQUIVALENCE OF JUNGCK-TYPE ITERATIONS FOR GENERALIZED CONTRACTIVE-LIKE OPERATORS IN A BANACH SPACE
We show that the convergences of Jungck, Jungck-
Mann, Jungck-Ishikawa, Jungck-Noor and Jungck-multistep itera-
tion processes are equivalent for a class of generalized contractive-
like operators defined on a Banach space. Our results are general-
izations and extensions of the work of Soltuz [20, 21], Zhiqun [23]
and some other numerous ones in literature
Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators
In this paper, we introduce Kirk-multistep and Kirk-multistep-SP iterative schemes and
prove their strong convergences and stabilities for contractive-type operators in
normed linear spaces. By taking numerical examples, we compare the convergence
speed of our schemes (Kirk-multistep-SP iterative schemes) with the others (Kirk-SP,
Kirk-Noor, Kirk-Ishikawa, Kirk-Mann and Kirk iterative schemes) for this class of
operators. Our results generalize and extend most convergence and stability results in
the literatur
Equivalence results for implicit Jungck–Kirk type iterations
We show that the implicit Jungck–Kirk-multistep, implicit Jungck–Kirk–Noor, implicit Jungck–Kirk–Ishikawa, and implicit Jungck–Kirk–Mann iteration schemes are equivalently used to approximate the common fixed points of a pair of weakly compatible generalized contractive-like operators defined on normed linear spaces. Our results contribute to the existing results on the equivalence of fixed point iteration schemes by extending them to pairs of maps. An example to show the applicability of the main results is included
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