Volume 3,  Issue 1, 2002

Article 3

APPROXIMATION OF FIXED POINTS OF ASYMPTOTICALLY DEMICONTRACTIVE MAPPINGS IN ARBITRARY BANACH SPACES

D.I. IGBOKWE

DEPARTMENT OF MATHEMATICS
UNIVERSITY OF UYO
UYO, NIGERIA
 E-Mail: EPSEELON@aol.com

Received 14 May, 2001; accepted 17 July, 2001.
Communicated by: S.S. Dragomir

ABSTRACT.    Let $E$ be a real Banach Space and $K$ a nonempty closed convex (not necessarily bounded) subset of $E$. Iterative methods for the approximation of fixed points of asymptotically demicontractive mappings $T:K \rightarrow K$ are constructed using the more general modified Mann and Ishikawa iteration methods with errors.

Our results show that a recent result of Osilike [1] (which is itself a generalization of a theorem of Qihou [2]) can be extended from real q-uniformly smooth Banach spaces, $1 < q < \infty$, to arbitrary real Banach spaces, and to the more general Modified Mann and Ishikawa iteration methods with errors. Furthermore, the boundedness assumption imposed on the subset $K$ in ([1], [2]) are removed in our present more general result. Moreover, our iteration parameters are independent of any geometric properties of the underlying Banach space.

Key words:
Asymptotically Demicontractive Maps, Fixed Points, Modified Mann and Ishikawa Iteration Methods with Errors. 

2000 Mathematics Subject Classification:
47H06, 47H10, 47H15, 47H17.

Download this article (PDF):

Suitable for a printer:    

Suitable for a monitor:        

 To view these files we recommend you save them to your file system and then view by using the Adobe Acrobat Reader. 

That is, click on the icon using the 2nd mouse button and select "Save Target As..." (Microsoft Internet Explorer) or "Save Link As..." (Netscape Navigator).

See our PDF pages for more information.

Other papers in this issue

Norm Inequalities in Star Algebras
A.K. Gaur

The Discrete Version of Ostrowski's Inequality in Normed Linear Spaces
S.S. Dragomir

Approximation of Fixed Points of Asymptotically Demicontractive Mappings in Arbitrary Banach Spaces-
D. I. Igbokwe

On an Identity for the Chebychev Functional and Some Ramifications
P. Cerone

L'Hospital Type Rules for Monotonicity, with Applications
Iosif Pinelis

Norms of Certain Operators on Weighted lp Spaces and Lorentz Sequence Spaces
G.J.O. Jameson and R. Lashkaripour 

L'Hospital Type Rules for Monotonicity: Applications to Probability Inequalities for Sums of Bounded Random Variables
Iosif Pinelis

On the value distribution of  j (z) [f (z)] n-1 f (k) (z)
Kit-Wing Yu

On Harmonic Functions by the Hadamard Product
M. Ozturk, S. Yalcin and M. Yamankaradeniz

Some Results on L1 Approximation of the r-th Derivate of Fourier Series
Zivorad Tomovski

On Grüss Type Integral Inequalities
Baburao G. Pachpatte

On Weighted Ostrowski Type Inequalities for Operators and Vector-valued Functions
 N.S.Barnett, C.Buse, P.Cerone and S.S.Dragomir 

A Generalisation of the Pre-Grüss Inequality and Applications to some Quadrature Formulae
N. Ujevic

Lower and Upper Solutions Method for First Order Differential Inclusions with Nonlinear Boundary Conditions
M.Benchohra and S.K. Ntouyas

An Integral Inequality Bounding the Autocorrelation of a Pulse or Sequence at a Known Lag
Robin Willink

Corrigendum on the paper ``An application of almost increasing and d- quasi-monotone sequences'' published in JIPAM, Vol.1, No.2. (2000), Article 18
H. Bor

 

Other issues
 

© 2000 School of Communications and Informatics, Victoria University of Technology. All rights reserved.
JIPAM is published by the School of Communications and Informatics which is part of the Faculty of Engineering and Science, located in Melbourne, Australia. All correspondence should be directed to the editorial office.

Copyright/Disclaimer