Common fixed point results for noncommuting mappings without continuity in cone metric spaces

By Mujahid Abbas, G. Jungck. 2008

592 citations recorded by the source corpus.

The existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions, without appealing to continuity, in a cone metric space is established. These results generalize several well-known comparable results in the literature.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/edd24b9f44ca0a0c0c75b4c685f505346db917a1

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In Geometry and Topology

1. Zoran Kadelburg
2. Stojan Radenovic
3. Mujahid Abbas
4. E. Karapınar
5. Bessem Samet
6. Wasfi A. Shatanawi
7. Pasquale Vetro
8. Nguyen Van Dung

Citations in the corpus

• Some Common Fixed Point Theorems in 0-σ-Complete Metric-Like Spaces (2013, background): “For the following definition and proposition we refer to [1].”
• QUASI-CONTRACTIONS ON SYMMETRIC AND CONE SYMMETRIC SPACES (2011, background): “Recently, in [1, 8, 9, 17], some common fixed point theorems have been proved for maps on cone metric spaces.”
• GENERALIZED CONE METRIC SPACES (2010, background): “The normality property of cone was an important ingredient in their results (see also, [1], and [2]).”
• Weakly φ-pairs and common fixed points in cone metric spaces (2009, background): “Also Abbas and Jungck [1] proved common fixed point theorems for a pair of weakly compatible maps.”
• Various generalizations of metric spaces and fixed point theorems (2015, background): “1 Let E = C1 R [0, 1], with ‖x‖ = ‖x‖∞ + ‖x ′‖∞, P = {x ∈ E : x(t) ≥ 0, t ∈ [0, 1]}.”
• ϕ-pairs and common fixed points in cone metric spaces (2008, background): “Also Abbas and Jungck [1] proved common fixed point theorems for a pair of weakly compatible maps.”
• BANACH CONTRACTION PRINCIPLE ON CONE RECTANGULAR METRIC SPACES (2009, background): “Subsequently, several other authors [1, 3, 4, 5] studied the existence of fixed points and common fixed points of mappings satisfying a contractive type condition on a normal cone metric space.”
• Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications (2015, background): “A large number of works are noted in [1, 2, 3, 8, 11, 12, 15, 17, 18, 20] and the relevant literature therein.”