IJPAM: Volume 63, No. 2 (2010)

WEAK AND STRONG CONVERGENCE THEOREMS
WITHOUT SOME WIDELY USED CONDITIONS

Safeer Hussain Khan$^1$, Hafiz Fukhar-Ud-Din$^2$
$^1$Department of Mathematics and Physics
College of Arts and Sciences
Qatar University
Doha, 2713, QATAR
e-mail: [email protected]
$^2$Department of Mathematics
The Islamia University of Bahawalpur
Bahawalpur, 63101, PAKISTAN
e-mail: [email protected]


Abstract.We establish weak (strong) convergence of Ishikawa iterates of two asymptotically (quasi-)nonexpansive maps without any condition on the rate of convergence associated with the two maps. Moreover, our weak convergence results do not require any of the Opial condition, Kadec-Klee property or Fréchet differentiable norm.

Received: May 27, 2010

AMS Subject Classification: 47H05, 47H10, 47H15, 49M05

Key Words and Phrases: asymptotically (quasi-)nonexpansive map, common fixed point, demiclosedness, Ishikawa iteration process, weak and strong convergence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 2