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Recommended by G ´ orniewicz Lech Here we introduce a generalisation of the Banach contraction mapping principle. We show that the result extends two existing generalisations of the same principle. We support our result by an example.
In this paper weak and strong convergence theorems of modified Noor iterations to fixed points for asymptotically nonexpansive map-pings in the intermediate sense in Banach spaces are established. In one theorem where we establish strong convergence we assume an additional property of the operator whereas in another theorem where we establish weak… (More)
In this work we introduce the class of weakly c-contractive mappings. We establish that these mappings necessarily have unique fixed points in complete metric spaces. We support our result by an example. Our result also generalises an existing result in metric spaces.
The study of fixed points of mappings satisfying certain contractive conditions has been at the center of rigorous research activity, see 1–3 . The notion ofD-metric space is a generalization of usual metric spaces and it is introduced by Dhage 4–7 . Recently, Mustafa and Sims 8, 9 have shown that most of the results concerning Dhage’sD-metric spaces are… (More)
In this paper we work out a unique common fixed point result for two self-mappings defined on a complete metric space. These mappings are assumed to satisfy a contractive inequality which involves two generalised altering distances.
In this paper we introduced the (E.A.)-property and weak compatibility of mappings in G-metric spaces. We have utilized these concepts to deduce certain common fixed point theorems in G-metric space
In this paper we establish some fixed point results for functions which satisfy certain weak contractive inequalities in partially ordered cone metric spaces. We have also given some illustrative examples. Our results are extension of some existing results. 1. Introduction Cone metric space is a recently introduced generalization of metric space where every… (More)
Here we prove a probabilistic contraction mapping principle in Menger spaces. This is in line with research in fixed point theory using control functions which was initiated by Khan et al. has also been constructed.