Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 24, No. 2, pp. 257-266 (2008)

Contractive conditions and common fixed points

Vyomesh Pant

Nainital, Uttarakhand, India

Abstract: In this paper we obtain common fixed point theorems under the Lipschitz type analogue of a strict contractive condition by using the notion of R-weak commutativity of type A_g. In the setting of our results, we use the property (E.A) introduced by Aamri and Moutawakil and compare these with the results proved by using the notion of noncompatiblity introduced by Pant. Simultaneously, we provide contractive condition which ensure the existence of a common fixed point; however, the mappings are discontinuous at the common fixed point.

Keywords: R-weak commutativity of type A_g, noncompatible maps, contractive condition, (E.A) property.

Classification (MSC2000): 54H25

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