An Extension of Gregus Fixed Point Theorem
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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)+ 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.
Banach spaces , Mathematics , Theorems , Fixed point theorems
Fixed Point Theory and Applications, 2007 (78628), 1-8