Some theorems on weakly contractive maps

By B. Rhoades. 2001

863 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/36f642334f9047e3223babc8449d36a7294b836d

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Coupled coincidence point theorems in ordered metric spaces (2011, background): “Subsequently, Rhoades [7] established that the result proved for weak contractions in [6] is also true in complete metric spaces.”
Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces (2011, background): “Rhoades [3] has shown that their result is still valid in complete metric spaces.”
SOME RESULTS ON WEAKLY CONTRACTIVE MAPS (2012, background): “[17] Let (X, d) be a complete metric space, and f be a φ-weak contraction on X for some φ ∈ Φ.”
Common fixed points for Ćirić type $f$-weak contraction with applications (2010, background): “A map T : X → X is called to be weakly contractive [1], [31] if, for each x, y ∈ X, d(Tx, Ty) ≤ d(x, y)− φ(d(x, y)), where φ : [0,∞) → [0,∞) is a lower semicontinuous function from the right such that φ is positive on (0,∞) and φ(0) = 0.”
A Fixed Point Theorem of Generalized Weakly Contractive Maps in Orbitally Complete Metric Spaces (2012, background): “[2] B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Analysis 47 (2001) 2683–2693.”
Fixed points of weak contractions in cone metric spaces (2010, background): “1 ([7]).”
Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition (2006, background): “Rhoades [14] extended some of their work to Banach spaces.”
Generalization of the Banach contraction principle (2013, background): “The above theorem has been generalized and extended in different directions see for example [1, 2, 5, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], and references therein.”
Solving variational inequalities involving nonexpansive type mappings (2008, neutral): “(Theorem 2, Rhoades [19]) Let C a nonempty closed convex subset of a Banach space X and f : C → C a weakly contraction mapping with the function ψ.”
Common Fixed Point of Multivalued Generalized -Weak Contractive Mappings (2010, result): “Our results extend previous results by Zhang and Song 2009 , as well as by Rhoades 2001 , Nadler 1969 , and Daffer and Kaneko 1995 .”