ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXIII, 1 (2004)
p. 119 – 126
On the Convergence of the Ishikawa Iteration in the Class of
Quasi Contractive Operators
V. Berinde
Abstract.
A convergence theorem of Rhoades \cite{rh2} 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 $\{\alpha_n\}$ that define the Ishikawa iteration are
also weakened.
AMS Subject classification: 47H10; 54H25
Keywords:
Banach space, quasi contraction,
fixed point, Ishikawa iteration, convergence theorem
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