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Title: An Extension of Gregus Fixed Point Theorem
Authors: Olaleru, J.O
Akewe, H
Keywords: Banach spaces
Fixed point theorems
Issue Date: 17-Dec-2006
Publisher: Hindawi Publishing Corporation
Citation: Fixed Point Theory and Applications, 2007 (78628), 1-8
Abstract: Let C be a closed convex subset of a complete metrizable topological vector space (X,d) and T :C→C a mapping that satisfies d(Tx,Ty)≤ad(x,y)+bd(x,Tx)+cd(y,Ty)+ ed(y,Tx)+ fd(x,Ty) for all x,y∈C, where 0<a<1, b≥0, c≥0, e≥0, f ≥0, and a+b+c+e+ f = 1. Then T has a unique fixed point. The above theorem, which is a generalization and an extension of the results of several authors, is proved in this paper. In addition, we use the Mann iteration to approximate the fixed point of T.
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