General constructive fixed point theorems for Ciric-type almost contractions in metric spaces


Vasile Berinde


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Existence and existence and uniqueness results for fixed points of single-valued Ciric almost contractions as well as convergence theorems for Picard iteration to these fixed points are proved. The Ciric type almost contraction condition appear to be one of the most general metrical condition for which the set of fixed points is not a singleton but the fixed points can be approximated by means of Picard iteration. Our results unify, generalize and extend most of the fundamental metrical fixed point theorems in literature (Banach, Kannan, Bianchini, Reich, Rus, Chatterjea, Rhoades, Hardy and Rogers, Zamfirescu, Ciric etc.) from the case of a unique fixed point to the case of non unique fixed points.

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Berinde, Vasile