[InlineEquation not available: see fulltext.]-Closed set and coupled coincidence point theorems for a generalized compatible in partially G-metric spaces

• Main Authors: Na Nan N., Charoensawan P.
• Format: Article
• Published: Springer Publishing Company 2015
• Subjects: Discrete Mathematics and Combinatorics; Applied Mathematics; Analysis
• Online Access: http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84930204480&origin=inward; http://cmuir.cmu.ac.th/handle/6653943832/38973
• Institution: Chiang Mai University

© 2014, Na Nan and Charoensawan; licensee Springer. In this work, we present a notion of an [InlineEquation not available: see fulltext.]-closed set and prove the existence of a coupled coincidence point theorem for a pair [InlineEquation not available: see fulltext.] of mappings [InlineEquation not available: see fulltext.] with φ-contraction mappings in partially ordered metric spaces without H-increasing property of F and mixed monotone property of H. We give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled coincidence point by H using the mixed monotone property and H-increasing property of F. We also show the uniqueness of a coupled coincidence point of the given mappings. Further, we apply our results to the existence and uniqueness of a coupled coincidence point of the given mappings in partially ordered G-metric spaces with H-increasing property of F and mixed monotone property of H. These results generalize some recent results in the literature.