On a fixed point theorem by totik  In this paper we prove a common fixed point theorem see Theorem 3.1 in metric spaces for two self-mappings satisfying a general implicit relation involving the diameter of nite sets, without requiring continuity. This theorem may be considered as a generalization of a result by Totik 1983. Also, it unies and generalizes some other results obtained by Fisher 1977, Akkouchi 2001 and Nova 1997.

Tipo de documento: Artículo - Article

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16(1), 21–32 (2009) 21 On a fixed point theorem by Totik Mohamed Akkouchi1 Faculté des Sciences–Semlalia Département de Mathématiques Université Cadi Ayyad, Avenue du Prince My.
Abdellah, B.P.
2390 Marrakech – Maroc – Morocco En este artı́culo se demuestra un teorema de punto fijo común (Teorema 3.1) en espacios métricos para dos auto–mapeos que satisfacen una relación implı́cita general que involucra el diámetro de conjuntos finitos sin exigir continuidad.
Este teorema se puede considerar como una generalización de un resultado de Totik (1983).
También, unifica y generaliza algunos otros resultados obtenidos por Fisher (1977), Akkouchi (2001) y Nova (1997). Palabras claves: Teoremas de punto fijo común en espacios métricos In this paper we prove a common fixed point theorem (see Theorem 3.1) in metric spaces for two self–mappings satisfying a general implicit relation involving the diameter of finite sets, without requiring continuity.
This theorem may be considered as a generalization of a result by Totik (1983). Also, it unifies and generalizes some other results obtained by Fisher (1977), Akkouchi (2001) and Nova (1997). Keywords: Common fixed point theorems in metric spaces. MSC: 54H25, 47H10 1 Introduction The common fixed point theory has seen a great developpement during the three last decades.
One can say that its story has started with the well known result of Markov and Kakutani. For two self–mappings S and T of a given metric space (X, d), many kind of contractive (exapnsive or nonexpansive) conditions may be considered.
We list here some examples. 1 akkouchimo@yahoo.fr 22 M.
Akkouchi, On a fixed poitn theorem d(Sx, Sy) ≤ q d(T x, T y) , ∀x, y ∈ X . (1.1) This condition generalizes the well known Banach contraction principle.
It has been generalized by the following condition d(Sx, Sy) ≤ q max{d(T x, T y), d(Sx, T x), d(Sy, T y), d(T x, Sy), d(T y, Sx)} . (1.2) A more general c...