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

Download:     Adobe PDF     Compressed Postscript      

Version to read:     Adobe PDF

Acta Mathematica Universitatis Comenianae
Institute of Applied Mathematics
Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

Telephone: + 421-2-60295755 Fax: + 421-2-65425882  
e-Mail: amuc@fmph.uniba.sk   Internet: www.iam.fmph.uniba.sk/amuc

© Copyright 2004, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE