On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered G‐Metric Spaces | Zendy

S. A. Mohiuddine | Zendy; Abdullah Alotaibi | Zendy

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On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered G‐Metric Spaces

Author(s) -

S. A. Mohiuddine,

Abdullah Alotaibi

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/897198

Subject(s) - mathematics , fixed point theorem , metric space , fixed point , uniqueness , monotone polygon , contraction mapping , nonlinear system , contraction (grammar) , fixed point property , pure mathematics , least fixed point , complete metric space , coincidence point , space (punctuation) , discrete mathematics , mathematical analysis , schauder fixed point theorem , picard–lindelöf theorem , geometry , computer science , medicine , quantum mechanics , operating system , physics

Two concepts—one of the coupled fixed point and the other of the generalized metric space—play a very active role in recent research on the fixed point theory. The definition of coupled fixed point was introduced by Bhaskar and Lakshmikantham (2006) while the generalized metric space was introduced by Mustafa and Sims (2006). In this work, we determine some coupled fixed point theorems for mixed monotone mapping satisfying nonlinear contraction in the framework of generalized metric space endowed with partial order. We also prove the uniqueness of the coupled fixed point for such mappings in this setup

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