The Australian Journal of Mathematical Analysis and Applications


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ISSN 1449-5910  

 

Paper Information

Paper Title:

Fixed Point Theorems for a Finite Family of Asymptotically Nonexpansive Mappings

Author(s):

E. Prempeh

Department of Mathematics,
Kwame Nkrumah University of Science and Technology,
Kumasi, Ghana
edward_prempeh2000@yahoo.com

Abstract:

Let be a real reflexive Banach space with a uniformly Gâteaux differentiable norm, be a nonempty bounded closed convex subset of i=1,2,...,r be a finite family of asymptotically nonexpansive mappings such that for each Let be a nonempty set of common fixed points of and define

. Let be fixed and let be such that as . We can prove that the sequence satisfying the relation

associated with , converges strongly to a fixed point of provided possesses uniform normal structure. Furthermore we prove that the iterative process:

, converges strongly to a fixed point of

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