An Extension of Gregus Fixed Point Theorem

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Olaleru, J.O
Akewe, H
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Hindawi Publishing Corporation
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.
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Fixed point , Convex subset , Complete metrizable , Topological space , Mann iteration , Research Subject Categories::MATHEMATICS
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.