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