Comments on the Paper by Gordji and Baghani Entitled ”a Generalization of Nadler’s Fixed Point Theorem”

We point out that the theorem of the paper listed in the title is a known result. 1. Main resultIn [1] the following theorem was proved.Theorem 1.1. Let (X, d) be a complete metric space, T : X → CB(X) such thatH(Tx, Ty) ≤αd(x, y) + β[D(x, Tx) + D(y, Ty)]+ γ[D(x, Ty) + D(y, Tx)]for all x, y ∈ X where α, β, γ ≥ 0, α + 2β + 2γ < 1. Then T has a fixed point.The theorem appears as Theorem 1 in [3]. It is a special case of [2], [5], [6],and [7]. The result has also been extended to uniform spaces in [4]. References[1] M.E. Gordji and H. Baghani, A generalization of Nadler’s fixed point theorem, J. NonlinearSci. and Appl., 3 (2010), 1148–151.[2] G. Garegnani and S. Massa, Multi-valued mappings of congtractive type, Ist. LombardoAccad. Sci. Rend A, 112 (1978), 283–288.[3] K. Iseki, Multi-valued contraction mappings in complete metric spaces, Rend. Sem. Mat.Univ. Padova, 53 (1975), 15–19.Date: Received: 18 May 2010.∗ Corresponding authorc© 2010 N.A.G.2000 Mathematics Subject Classification. Primary: 47H10.