APPROXIMATING FIXED POINTS OF WEAK '-CONTRACTIONS USING THE PICARD ITERATION

By Vasile Berinde. 2003

372 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2ad6414a2c477b1c1327f899b5279e0df9e5ffba

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Citations in the corpus

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].”
On a general class of multi-valued weakly Picard mappings (2007, background): “14) where θ ∈ (0,1) and L1 0 are two constants, then even in the single-valued case, see [7], T need not have a fixed point.”
SOME RESULTS ON WEAKLY CONTRACTIVE MAPS (2012, background): “Some other works related to the concept of weak contractions are [1, 5, 9, 14].”
On the approximation of fixed points of weak contractive mappings (2003, methodology): “Some convergence theorems for the Picard iteration in various classes of contractive type mappings, are also obtain as corollaries of the main results in [3] and [4].”
Large Contractions on Quasi-Metric Spaces with an Application to Nonlinear Fractional Differential Equations (2019, methodology): “In the present paper, inspired from the result of Berinde [1] and Popescu [3], we propose a new contraction, and then we discuss fixed point existence problems for such mappings.”
Approximating fixed points of enriched contractions in Banach spaces (2019, background): “Picard-Banach contractions have been previously extended in [3] to the so called almost contractions, a class of mappings which preserve most of the features of Picard-Banach contractions but may have more than one fixed point, see also [1], [5], [9] and references therein.”
APPROXIMATING COMMON FIXED POINTS OF NONCOMMUTING ALMOST CONTRACTIONS IN METRIC SPACES (2010, background): “3 we obtain the existence and uniqueness fixed point theorem given in [6] for almost contractions (Theorem 2).”
On coincidence point and fixed point theorems for nonlinear multivalued maps (2012, background): “In particular, if there exists B ∈ [0,∞) such that b(x) = B for all x ∈ X , then T is called a Berinde map [13,15].”