Data Dependence for Ishikawa Iteration When Dealing with Contractive-Like Operators
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چکیده
منابع مشابه
On the Convergence of the Ishikawa Iteration in the Class of Quasi Contractive Operators
A convergence theorem of Rhoades [18] regarding the approximation of fixed points of some quasi contractive operators in uniformly convex Banach spaces using the Ishikawa iterative procedure, is extended to arbitrary Banach spaces. The conditions on the parameters {αn} that define the Ishikawa iteration are also weakened.
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We show that the convergences of Jungck, JungckMann, Jungck-Ishikawa, Jungck-Noor and Jungck-multistep iteration processes are equivalent for a class of generalized contractivelike operators defined on a Banach space. Our results are generalizations and extensions of the work of Soltuz [20, 21], Zhiqun [23] and some other numerous ones in literature.
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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 im...
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تاریخ انتشار 2008