An Extension of Gregus Fixed Point Theorem
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Date
2006-12-17
Authors
Olaleru, J.O
Akewe, H
Journal Title
Journal ISSN
Volume Title
Publisher
Hindawi Publishing Corporation
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.
Description
Keywords
Banach spaces , Mathematics , Theorems , Fixed point theorems
Citation
Fixed Point Theory and Applications, 2007 (78628), 1-8