An Extension of Gregus Fixed Point Theorem
نویسنده
چکیده
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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