On the approximation of fixed points of weak contractive mappings

By Vasile Berinde. 2003

183 citations recorded by the source corpus.

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Citations in the corpus

APPROXIMATING COMMON FIXED POINTS OF NONCOMMUTING ALMOST CONTRACTIONS IN METRIC SPACES (2010, background): “As the Zamfirescu fixed point theorem was extended to the class of almost contraction - a large class of contractive type mappings introduced in [6] and also studied in [3], [2] and in many other papers, see [9] and the bibliography therein - the main aim of the present paper is to extend the result”
On a general class of multi-valued weakly Picard mappings (2007, background): “Therefore, Theorem 2 includes as particular cases several important fixed point theorems in literature, amongst them we mention: the contraction mapping principle, Kannan fixed point theorem [17], Zamfirescu’s fixed point theorem [39] and many other fixed point theorems, see [6,33,35] for more detai”
Data dependence results of new multi-step and S-iterative schemes for contractive-like operators (2012, background): “[35] V. Berinde, ”Iterative Approximation of Fixed Points ”, Springer, Berlin (2007).”
SOME FIXED POINT RESULTS FOR A NEW THREE STEPS ITERATION PROCESS IN BANACH SPACES (2017, unknown): “[4] Let (X, d) be a complete metric space and T : X → X be a weak contraction for which there exist δ ∈ (0, 1) and some L1 ≥ 0 such that ‖Tx− Ty‖ ≤ δ ‖x− y‖+ L1 ‖x− Tx‖ .”
Ćirić type generalized F-contractions on complete metric spaces and fixed point results (2014, methodology): “In [3] and [4], Berinde shows that any Banach, Kannan, Chatterjea and Zamfirescu mappings are almost contraction.”
Common fixed points of mappings satisfying implicit contractive conditions (2012, unknown): “Berinde in [7-15] obtained (common) fixed point theorems, which were called constructive (common) fixed point theorems, see [12].”