| Abstract |
will denote the set of natural numbers including zero over the course of this study. Let C be a nonempty subset of a Banach space B and S,T:C→C be two mappings with T(C)⊆S(C). Then, we denote the set of all fixed points of T by F_T and the set of common fixed points of S and T by F.
It is now considered indisputable that iteration methods are among the most important and useful mathematical tools which are used in solving a wide variety of problems arise in mathematics and other branches of science.
In this study, we introduce a Modified Jungck-Picard-S hybrid type iterative methods as follows:
{■(x_0∈C,@Sx_(n+1)=T^n y_n,@Sy_n=(1-α_n^0 ) T^n x_n+α_n^0 T^n z_n,@Sz_n=(1-α_n^1 )Sx_n+α_n^1 T^n x_n,n∈ ,)┤ (1)
where {α_n^i }_(n=0)^∞,i=(0,1) ̅, are real sequences in [0,1] satisfying certain control condition(s).
We establish weak stability, weak convergence and strong convergence results for a pair of Jungck asymptotically nonexpansive mappings with the help of the Modified Jungck-Picard-S iterative procedure. An illustrative example is also discussed to show that the iterative procedure (1) converges faster than some iterative procedures in the existing literature.
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