An Extension of Gregus Fixed Point Theorem

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Date
2007
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) + f d(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
Staff publications
Keywords
Fixed point , Convex subset , Complete metrizable , Topological space , Mann iteration , Research Subject Categories::MATHEMATICS
Citation
Olaleru, J.O and Akewe, H. (2007). An Extension of Gregus Fixed Point Theorem. Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007, Article ID 78628, 8.