IJPAM: Volume 19, No. 4 (2005)

STRONG CONVERGENCE THEOREMS FOR
$k$-STRICTLY ASYMPTOTICALLY
PSEUDOCONTRACTIVE AND
HEMICONTRACTIVE OPERATORS IN
ARBITRARY REAL NORMED LINEAR SPACES

Olusegun O. Owojori
Department of Mathematics
Obafemi Awolowo University
Ile-Ife, NIGERIA
e-mail: walejori@oauife.edu.ng


Abstract.In this work, we establish strong convergence of the revised modified three-step iteration methods for $k$-strictly asymptotically pseudocontractive and hemicontractive operators in arbitrary real normed linear spaces. Our results extend the previous results for asymptotically nonexpansive mappings and those of Liu Qihou [10], which itself is an extension of those of Schu [11], for asymptotically pseudocontractive mappings to the modified three-step iteration methods.

Received: January 24, 2005

AMS Subject Classification: 47H04, 47H06, 47H10

Key Words and Phrases: three-step iteration methods, $k$-strictly asymptotically pseudocontractive operators, hemicontractive operators, real normed linear space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 19
Issue: 4